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Консультация № 201294
25.07.2021, 14:25
0.00 руб.
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1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
"Найти наибольшее и наименьшее значения функции z=(2x^2)+2xy-(0,5y^2)-4x в области D: y=2x, y=2, x=0."
"Найти наибольшее и наименьшее значения функции z=(2x^2)+2xy-(0,5y^2)-4x в области D: y=2x, y=2, x=0."
Обсуждение
25.07.2021, 15:12
общий
это ответ
1) Построим, заданную область 
, ограниченную линиями 
(см.изображение)
2) Найдем стационарные точки заданной функции и вычислим значения функции в них.
3) Исследуем границы области:
a) левая сторона треугольника (
):
исследуем второй конец отрезка - точку
б) верхняя сторона треугольника (
):
точка уже исследована
исследуем второй конец отрезка - точку
в) нижняя сторона треугольника (
):
точка
уже исследована
концы отрезка - точки
и - уже исследованы
4) Имеем:
значит,
Ответ:
, ограниченную линиями (см.изображение)2) Найдем стационарные точки заданной функции и вычислим значения функции в них.
3) Исследуем границы области
:a) левая сторона треугольника (
):исследуем второй конец отрезка - точку
б) верхняя сторона треугольника (
):точка
уже исследованаисследуем второй конец отрезка - точку
в) нижняя сторона треугольника (
):точка
уже исследованаконцы отрезка - точки
и - уже исследованы4) Имеем:
значит,
Ответ:
Прикрепленные файлы:
5
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