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Страница 89, часть 2 - гдз по алгебре 10 класс учебник часть 1, 2 Пак, Ардакулы
Авторы: Пак О. В., Ардакулы Д., Ескендирова Е. В.
Тип: Учебник
Издательство: Алматыкітап баспасы
Год издания: 2019 - 2026
Часть: 2
ISBN: 978-601-01-3958-9
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 10 классе
Часть 2. Cтраница 89
App\Models\BookPage {#1003 // resources/views/models/book_page/default.blade.php #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1099242 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "89" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/page-2-89" "field_display_title" => "89" "field_folder" => "2" "field_image_name" => "89" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1015 #items: array:1 [ 0 => App\Models\Branch {#1014 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1119426 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1019 #items: array:1 [ 0 => App\Models\Term {#1016 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ 0 => App\Models\Book {#1018 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4295 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1020 #items: array:1 [ 0 => App\Models\Term {#1017 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1021 #items: array:1 [ 0 => App\Models\Term {#1022 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1023 #items: array:1 [ 0 => App\Models\Term {#1024 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7006 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Алматыкітап баспасы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almatykitap baspasy" ] #original: array:6 [ "id" => 7006 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Алматыкітап баспасы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almatykitap baspasy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1025 #items: array:3 [ 0 => App\Models\Term {#1026 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7007 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Пак" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Олег" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #original: array:12 [ "id" => 7007 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Пак" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Олег" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1027 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7008 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Ардакулы" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Дархан" "field_patronymic" => null "field_surname_rp" => null ] #original: array:12 [ "id" => 7008 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Ардакулы" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Дархан" "field_patronymic" => null "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1028 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7009 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Ескендирова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7009 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Ескендирова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1029 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ 0 => App\Models\Term {#1031 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1032 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1037 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1038 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1041 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 10 класса общеобразовательной школы общественно-гуманитарного направления" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1063" "field_priority" => "6" "field_default_folder" => "/algebra_10/baspasy-u19/" "field_isbn" => "978-601-01-3958-9" "field_cover" => array:1 [ 0 => "/media/algebra_10/baspasy-u19/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_10/baspasy-u19/covers/cover1.webp" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1044 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1045 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 542 "class_subject" => 387 ] ] #original: array:50 [ "id" => 4295 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1020} "field_class" => Illuminate\Database\Eloquent\Collection {#1021} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1023} "field_author" => Illuminate\Database\Eloquent\Collection {#1025} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1029} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1030} "field_country" => Illuminate\Database\Eloquent\Collection {#1032} "field_city" => Illuminate\Database\Eloquent\Collection {#1034} "field_series" => Illuminate\Database\Eloquent\Collection {#1036} "field_umk" => Illuminate\Database\Eloquent\Collection {#1037} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1038} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1039} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1040} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1041} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 10 класса общеобразовательной школы общественно-гуманитарного направления" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1063" "field_priority" => "6" "field_default_folder" => "/algebra_10/baspasy-u19/" "field_isbn" => "978-601-01-3958-9" "field_cover" => array:1 [ 0 => "/media/algebra_10/baspasy-u19/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_10/baspasy-u19/covers/cover1.webp" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1042} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1043} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1044} "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1045} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 542 "class_subject" => 387 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1046 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1119426 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1019} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1048} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1046} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1006 #items: array:1 [ 0 => App\Models\Book {#1018} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1007 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Element {#1051 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1262667 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Edition {#1061 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4962 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1063 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4962 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1066} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1070} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1064} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1067} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1099242" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "89-1.jpg" "alt" => null "width" => "2125" "height" => 3034 "path" => "/media/algebra_10/baspasy-u19/0-2/89-1.webp?ts=1752153892" ] ] ] #original: array:6 [ "id" => 1262667 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1062} "book_page" => array:2 [ "refs" => "1099242" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "89-1.jpg" "alt" => null "width" => "2125" "height" => 3034 "path" => "/media/algebra_10/baspasy-u19/0-2/89-1.webp?ts=1752153892" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => Illuminate\Database\Eloquent\Collection {#3713 #items: array:1 [ 0 => App\Models\BookPage {#3708 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1099243 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/page-2-90" "field_display_title" => "90" "field_folder" => "2" "field_image_name" => "90" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#3711 #items: array:1 [ 0 => App\Models\Branch {#1113 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1119426 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Term {#1016} ] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Book {#1018} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1119426 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1114} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1115} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#3714 #items: array:1 [ 0 => App\Models\Book {#1018} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#3712 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3728 #items: array:1 [ 0 => App\Models\Element {#3727 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1262668 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#3729 #items: array:1 [ 0 => App\Models\Edition {#1061} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "90-1.jpg" "alt" => null "width" => "2125" "height" => 3034 "path" => "/media/algebra_10/baspasy-u19/0-2/90-1.webp?ts=1752153892" ] ] ] #original: array:6 [ "id" => 1262668 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#3729} "book_page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "90-1.jpg" …4 ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1099244" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1099242" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#3721 #items: array:6 [ 0 => App\Models\Task {#3737 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120339 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3738 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3739 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3740 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#3741 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3743 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120340" "type" => "task" ] "previous" => array:2 [ "refs" => "1120338" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3749 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120339 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3738} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3739} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3740} "parent_branches" => Illuminate\Database\Eloquent\Collection {#3741} "content" => Illuminate\Database\Eloquent\Collection {#3743} "next" => array:2 [ "refs" => "1120340" "type" => "task" ] "previous" => array:2 [ "refs" => "1120338" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3749} "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#3744 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120340 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3742 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3751 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3747 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#3745 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3746 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120341" "type" => "task" ] "previous" => array:2 [ "refs" => "1120339" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3761 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120340 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3742} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3751} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3747} "parent_branches" => Illuminate\Database\Eloquent\Collection {#3745} "content" => Illuminate\Database\Eloquent\Collection {#3746} "next" => array:2 [ "refs" => "1120341" "type" => "task" ] "previous" => array:2 [ "refs" => "1120339" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3761} "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#3756 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120341 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3748 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3763 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3759 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#3757 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3758 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120342" "type" => "task" ] "previous" => array:2 [ "refs" => "1120340" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3773 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120341 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3748} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3763} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3759} "parent_branches" => Illuminate\Database\Eloquent\Collection {#3757} "content" => Illuminate\Database\Eloquent\Collection {#3758} "next" => array:2 [ "refs" => "1120342" "type" => "task" ] "previous" => array:2 [ "refs" => "1120340" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3773} "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#3768 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120342 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3760 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3775 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3771 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#3769 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3770 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120343" "type" => "task" ] "previous" => array:2 [ "refs" => "1120341" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3785 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120342 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3760} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3775} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3771} "parent_branches" => Illuminate\Database\Eloquent\Collection {#3769} "content" => Illuminate\Database\Eloquent\Collection {#3770} "next" => array:2 [ "refs" => "1120343" "type" => "task" ] "previous" => array:2 [ "refs" => "1120341" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3785} "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#3780 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120343 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3772 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3787 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3783 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#3781 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3782 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120344" "type" => "task" ] "previous" => array:2 [ "refs" => "1120342" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3797 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120343 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#3772} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3787} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3783} "parent_branches" => Illuminate\Database\Eloquent\Collection {#3781} "content" => Illuminate\Database\Eloquent\Collection {#3782} "next" => array:2 [ "refs" => "1120344" "type" => "task" ] "previous" => array:2 [ "refs" => "1120342" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3797} "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#3792 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120344 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => "91" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-7" "field_display_title" => "7" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#3784 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3799 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3795 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#3793 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3794 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120345" "type" => "task" ] "previous" => array:2 [ "refs" => "1120343" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3809 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120344 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_page_end" => "91" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-7" "field_display_title" => "7" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#3784} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#3799} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#3795} "parent_branches" => Illuminate\Database\Eloquent\Collection {#3793} "content" => Illuminate\Database\Eloquent\Collection {#3794} "next" => array:2 [ "refs" => "1120345" "type" => "task" ] "previous" => array:2 [ "refs" => "1120343" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#3809} "page" => array:2 [ "refs" => "1099243" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1099243 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "90" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/page-2-90" "field_display_title" => "90" "field_folder" => "2" "field_image_name" => "90" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#3711} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#3714} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#3712} "content" => Illuminate\Database\Eloquent\Collection {#3728} "next" => array:2 [ "refs" => "1099244" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1099242" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#3721} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "previous" => Illuminate\Database\Eloquent\Collection {#3704 #items: array:1 [ 0 => App\Models\BookPage {#3703 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1099241 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "88" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/page-2-88" "field_display_title" => "88" "field_folder" => "2" "field_image_name" => "88" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#3705 #items: array:1 [ 0 => App\Models\Branch {#1113} ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#3706 #items: array:1 [ 0 => App\Models\Book {#1018} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#3707 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#3717 #items: array:1 [ 0 => App\Models\Element {#3716 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1262666 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#3718 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1099241" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1262666 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#3718} "book_page" => array:2 [ "refs" => "1099241" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1099242" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1099240" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#3709 #items: [] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1099241 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "88" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/page-2-88" "field_display_title" => "88" "field_folder" => "2" "field_image_name" => "88" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#3705} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#3706} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#3707} "content" => Illuminate\Database\Eloquent\Collection {#3717} "next" => array:2 [ "refs" => "1099242" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1099240" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#3709} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "tasks" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Task {#1055 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1120338 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "89" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ 0 => App\Models\Branch {#1014} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:3 [ 0 => App\Models\Branch {#1113} 1 => App\Models\Branch {#1117 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1119442 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Применение производной" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "76" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1119442 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Применение производной" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "76" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1120} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1122 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1119446 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Экстремумы и критические точки" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "86" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1119446 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Экстремумы и критические точки" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1126} "field_page_start" => "86" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1125} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:2 [ 0 => App\Models\Element {#1095 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1301023 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ …1] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1120338" "type" => "task" ] "text" => "<p>Всюду в данном наборе задач и далее при определении точек экстремума необходимо указывать, является ли данная точка экстремума точкой максимума или точкой минимума.</p><p><strong>1.</strong> (1) На рисунке 3 изображен график функции $y=f(x)$, $D(f):(-7;7)$.</p><svg viewBox="-75 -35 150 70" xmlns="http://www.w3.org/2000/svg" font-family="sans-serif"><!-- Minor grid lines (every 1 unit, 1 unit = 10px) --><g stroke="#eee" stroke-width="0.25"><line x1="-70" y1="-30" x2="70" y2="-30"/><line x1="-70" y1="-20" x2="70" y2="-20"/><line x1="-70" y1="-10" x2="70" y2="-10"/><line x1="-70" y1="10" x2="70" y2="10"/><line x1="-70" y1="20" x2="70" y2="20"/><line x1="-70" y1="30" x2="70" y2="30"/><line x1="-60" y1="-30" x2="-60" y2="30"/><line x1="-50" y1="-30" x2="-50" y2="30"/><line x1="-40" y1="-30" x2="-40" y2="30"/><line x1="-30" y1="-30" x2="-30" y2="30"/><line x1="-20" y1="-30" x2="-20" y2="30"/><line x1="-10" y1="-30" x2="-10" y2="30"/><line x1="10" y1="-30" x2="10" y2="30"/><line x1="20" y1="-30" x2="20" y2="30"/><line x1="30" y1="-30" x2="30" y2="30"/><line x1="40" y1="-30" x2="40" y2="30"/><line x1="50" y1="-30" x2="50" y2="30"/><line x1="60" y1="-30" x2="60" y2="30"/><line x1="70" y1="-30" x2="70" y2="30"/></g><!-- Major grid lines (every 2 units, bolder) --><g stroke="#ccc" stroke-width="0.5"><line x1="-70" y1="-20" x2="70" y2="-20"/><line x1="-70" y1="20" x2="70" y2="20"/><line x1="-60" y1="-30" x2="-60" y2="30"/><line x1="-40" y1="-30" x2="-40" y2="30"/><line x1="-20" y1="-30" x2="-20" y2="30"/><line x1="20" y1="-30" x2="20" y2="30"/><line x1="40" y1="-30" x2="40" y2="30"/><line x1="60" y1="-30" x2="60" y2="30"/></g><!-- Axes --><line x1="-70" y1="0" x2="70" y2="0" stroke="black" stroke-width="1"/><line x1="0" y1="-30" x2="0" y2="30" stroke="black" stroke-width="1"/><!-- Axis labels --><text x="73" y="5" font-size="8" fill="black">x</text><text x="-5" y="35" font-size="8" fill="black">y</text><text x="3" y="-3" font-size="8" fill="black">O</text><!-- Red curve --><polyline fill="none" stroke="red" stroke-width="2" points="-70,-25 -40,20 -20,-10 0,10 20,0 40,20 50,10 70,30"/><!-- Dashed line --><line x1="-60" y1="10" x2="60" y2="10" stroke="#999" stroke-dasharray="5,5" stroke-width="1"/><!-- Text for dashed line --><text x="-30" y="17" font-size="7" fill="black">касательная в х=0</text></svg><p>Рис. 3</p><p><strong>а)</strong> Укажите все критические точки функции $f(x)$.</p><p><strong>б)</strong> Укажите точки локальных экстремумов.</p><p><strong>в)</strong> Решите неравенства $f'(x)\leq0, f'(x)<0, f'(x)\geq0, f'(x)>0$.</p>" "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:7 [ "id" => 1301023 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094} "task" => array:2 [ "refs" => "1120338" "type" => "task" ] "text" => "<p>Всюду в данном наборе задач и далее при определении точек экстремума необходимо указывать, является ли данная точка экстремума точкой максимума или точкой минимума.</p><p><strong>1.</strong> (1) На рисунке 3 изображен график функции $y=f(x)$, $D(f):(-7;7)$.</p><svg viewBox="-75 -35 150 70" xmlns="http://www.w3.org/2000/svg" font-family="sans-serif"><!-- Minor grid lines (every 1 unit, 1 unit = 10px) --><g stroke="#eee" stroke-width="0.25"><line x1="-70" y1="-30" x2="70" y2="-30"/><line x1="-70" y1="-20" x2="70" y2="-20"/><line x1="-70" y1="-10" x2="70" y2="-10"/><line x1="-70" y1="10" x2="70" y2="10"/><line x1="-70" y1="20" x2="70" y2="20"/><line x1="-70" y1="30" x2="70" y2="30"/><line x1="-60" y1="-30" x2="-60" y2="30"/><line x1="-50" y1="-30" x2="-50" y2="30"/><line x1="-40" y1="-30" x2="-40" y2="30"/><line x1="-30" y1="-30" x2="-30" y2="30"/><line x1="-20" y1="-30" x2="-20" y2="30"/><line x1="-10" y1="-30" x2="-10" y2="30"/><line x1="10" y1="-30" x2="10" y2="30"/><line x1="20" y1="-30" x2="20" y2="30"/><line x1="30" y1="-30" x2="30" y2="30"/><line x1="40" y1="-30" x2="40" y2="30"/><line x1="50" y1="-30" x2="50" y2="30"/><line x1="60" y1="-30" x2="60" y2="30"/><line x1="70" y1="-30" x2="70" y2="30"/></g><!-- Major grid lines (every 2 units, bolder) --><g stroke="#ccc" stroke-width="0.5"><line x1="-70" y1="-20" x2="70" y2="-20"/><line x1="-70" y1="20" x2="70" y2="20"/><line x1="-60" y1="-30" x2="-60" y2="30"/><line x1="-40" y1="-30" x2="-40" y2="30"/><line x1="-20" y1="-30" x2="-20" y2="30"/><line x1="20" y1="-30" x2="20" y2="30"/><line x1="40" y1="-30" x2="40" y2="30"/><line x1="60" y1="-30" x2="60" y2="30"/></g><!-- Axes --><line x1="-70" y1="0" x2="70" y2="0" stroke="black" stroke-width="1"/><line x1="0" y1="-30" x2="0" y2="30" stroke="black" stroke-width="1"/><!-- Axis labels --><text x="73" y="5" font-size="8" fill="black">x</text><text x="-5" y="35" font-size="8" fill="black">y</text><text x="3" y="-3" font-size="8" fill="black">O</text><!-- Red curve --><polyline fill="none" stroke="red" stroke-width="2" points="-70,-25 -40,20 -20,-10 0,10 20,0 40,20 50,10 70,30"/><!-- Dashed line --><line x1="-60" y1="10" x2="60" y2="10" stroke="#999" stroke-dasharray="5,5" stroke-width="1"/><!-- Text for dashed line --><text x="-30" y="17" font-size="7" fill="black">касательная в х=0</text></svg><p>Рис. 3</p><p><strong>а)</strong> Укажите все критические точки функции $f(x)$.</p><p><strong>б)</strong> Укажите точки локальных экстремумов.</p><p><strong>в)</strong> Решите неравенства $f'(x)\leq0, f'(x)<0, f'(x)\geq0, f'(x)>0$.</p>" "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1093 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1552059 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ …1] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1120338" "type" => "task" ] "text" => "<p><strong>а)</strong> Критическими точками функции являются внутренние точки области определения, в которых производная функции равна нулю или не существует.</p><p>Из графика видно, что касательная к графику функции горизонтальна (а значит, производная $f'(x)=0$) в точках локального максимума $x=-4$ и локального минимума $x=5$.</p><p>В точках $x=-2$ и $x=2$ график функции имеет изломы (острые пики), в таких точках производная не существует.</p><p>Таким образом, все критические точки функции на интервале $(-7; 7)$ — это $x=-4, x=-2, x=2, x=5$.</p><p><strong>Ответ:</strong> $-4, -2, 2, 5$.</p><p><strong>б)</strong> Точки локальных экстремумов — это точки, в которых производная меняет знак. Они находятся среди критических точек.</p><p>Проанализируем поведение функции в окрестности каждой критической точки:</p><p>1. В точке $x=-4$ возрастание функции сменяется убыванием, следовательно, $x=-4$ — точка локального максимума.</p><p>2. В точке $x=-2$ убывание функции сменяется возрастанием, следовательно, $x=-2$ — точка локального минимума.</p><p>3. В точке $x=2$ возрастание функции сменяется убыванием, следовательно, $x=2$ — точка локального максимума.</p><p>4. В точке $x=5$ убывание функции сменяется возрастанием, следовательно, $x=5$ — точка локального минимума.</p><p><strong>Ответ:</strong> $x_{max}=-4$ (точка максимума), $x_{min}=-2$ (точка минимума), $x_{max}=2$ (точка максимума), $x_{min}=5$ (точка минимума).</p><p><strong>в)</strong> Знак производной $f'(x)$ связан с монотонностью функции $f(x)$. Если функция возрастает, то $f'(x) > 0$. Если функция убывает, то $f'(x) < 0$.</p><p>Исходя из графика, определим промежутки монотонности функции:</p><p>• Функция возрастает на интервалах $(-7; -4)$, $(-2; 2)$ и $(5; 7)$.</p><p>• Функция убывает на интервалах $(-4; -2)$ и $(2; 5)$.</p><p>• Производная равна нулю в точках $x=-4$ и $x=5$.</p><p>• Производная не существует в точках $x=-2$ и $x=2$.</p><p>На основе этого решим неравенства:</p><p>• $f'(x) \le 0$: функция убывает или ее производная равна нулю. Это объединение интервалов $(-4; -2)$, $(2; 5)$ и точек $x=-4, x=5$.</p><p>• $f'(x) < 0$: функция строго убывает на интервалах $(-4; -2)$ и $(2; 5)$.</p><p>• $f'(x) \ge 0$: функция возрастает или ее производная равна нулю. Это объединение интервалов $(-7; -4)$, $(-2; 2)$, $(5; 7)$ и точек $x=-4, x=5$.</p><p>• $f'(x) > 0$: функция строго возрастает на интервалах $(-7; -4)$, $(-2; 2)$ и $(5; 7)$.</p><p>Ответ:<br>$f'(x) \le 0$ при $x \in [-4; -2) \cup (2; 5]$;<br>$f'(x) < 0$ при $x \in (-4; -2) \cup (2; 5)$;<br>$f'(x) \ge 0$ при $x \in (-7; -4] \cup (-2; 2) \cup [5; 7)$;<br>$f'(x) > 0$ при $x \in (-7; -4) \cup (-2; 2) \cup (5; 7)$.</p>" ] #original: array:6 [ "id" => 1552059 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080} "task" => array:2 [ "refs" => "1120338" "type" => "task" ] "text" => "<p><strong>а)</strong> Критическими точками функции являются внутренние точки области определения, в которых производная функции равна нулю или не существует.</p><p>Из графика видно, что касательная к графику функции горизонтальна (а значит, производная $f'(x)=0$) в точках локального максимума $x=-4$ и локального минимума $x=5$.</p><p>В точках $x=-2$ и $x=2$ график функции имеет изломы (острые пики), в таких точках производная не существует.</p><p>Таким образом, все критические точки функции на интервале $(-7; 7)$ — это $x=-4, x=-2, x=2, x=5$.</p><p><strong>Ответ:</strong> $-4, -2, 2, 5$.</p><p><strong>б)</strong> Точки локальных экстремумов — это точки, в которых производная меняет знак. Они находятся среди критических точек.</p><p>Проанализируем поведение функции в окрестности каждой критической точки:</p><p>1. В точке $x=-4$ возрастание функции сменяется убыванием, следовательно, $x=-4$ — точка локального максимума.</p><p>2. В точке $x=-2$ убывание функции сменяется возрастанием, следовательно, $x=-2$ — точка локального минимума.</p><p>3. В точке $x=2$ возрастание функции сменяется убыванием, следовательно, $x=2$ — точка локального максимума.</p><p>4. В точке $x=5$ убывание функции сменяется возрастанием, следовательно, $x=5$ — точка локального минимума.</p><p><strong>Ответ:</strong> $x_{max}=-4$ (точка максимума), $x_{min}=-2$ (точка минимума), $x_{max}=2$ (точка максимума), $x_{min}=5$ (точка минимума).</p><p><strong>в)</strong> Знак производной $f'(x)$ связан с монотонностью функции $f(x)$. Если функция возрастает, то $f'(x) > 0$. Если функция убывает, то $f'(x) < 0$.</p><p>Исходя из графика, определим промежутки монотонности функции:</p><p>• Функция возрастает на интервалах $(-7; -4)$, $(-2; 2)$ и $(5; 7)$.</p><p>• Функция убывает на интервалах $(-4; -2)$ и $(2; 5)$.</p><p>• Производная равна нулю в точках $x=-4$ и $x=5$.</p><p>• Производная не существует в точках $x=-2$ и $x=2$.</p><p>На основе этого решим неравенства:</p><p>• $f'(x) \le 0$: функция убывает или ее производная равна нулю. Это объединение интервалов $(-4; -2)$, $(2; 5)$ и точек $x=-4, x=5$.</p><p>• $f'(x) < 0$: функция строго убывает на интервалах $(-4; -2)$ и $(2; 5)$.</p><p>• $f'(x) \ge 0$: функция возрастает или ее производная равна нулю. Это объединение интервалов $(-7; -4)$, $(-2; 2)$, $(5; 7)$ и точек $x=-4, x=5$.</p><p>• $f'(x) > 0$: функция строго возрастает на интервалах $(-7; -4)$, $(-2; 2)$ и $(5; 7)$.</p><p>Ответ:<br>$f'(x) \le 0$ при $x \in [-4; -2) \cup (2; 5]$;<br>$f'(x) < 0$ при $x \in (-4; -2) \cup (2; 5)$;<br>$f'(x) \ge 0$ при $x \in (-7; -4] \cup (-2; 2) \cup [5; 7)$;<br>$f'(x) > 0$ при $x \in (-7; -4) \cup (-2; 2) \cup (5; 7)$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1120339" "type" => "task" ] "previous" => array:2 [ "refs" => "1120337" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Book {#1018} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1099242" "type" => "book_page" ] ] #original: array:24 [ "id" => 1120338 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "89" "field_page_end" => null "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/6-2zad-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1057} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1059} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1056} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1103} "content" => Illuminate\Database\Eloquent\Collection {#1065} "next" => array:2 [ "refs" => "1120339" "type" => "task" ] "previous" => array:2 [ "refs" => "1120337" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1098} "page" => array:2 [ "refs" => "1099242" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1099242 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "89" "field_url" => "/10-klass/algebra/baspasy-pak-uchebnik/page-2-89" "field_display_title" => "89" "field_folder" => "2" "field_image_name" => "89" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1015} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1006} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1007} "content" => Illuminate\Database\Eloquent\Collection {#1052} "next" => array:2 [ "refs" => "1099243" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1099241" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1053} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
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