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Консультация № 191293
22.08.2017, 10:37
0.00 руб.
0
4
1
Здравствуйте! Прошу помощи в решении:
Исследовать на экстремум функцию z = f(x, y)
z = 2x – 8y – x2 – y2 – 9.
Исследовать на экстремум функцию z = f(x, y)
z = 2x – 8y – x2 – y2 – 9.
Обсуждение
22.08.2017, 11:30
общий
Адресаты:
Почему бы не оформить ответ? 
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
22.08.2017, 19:00
общий
это ответ
Здравствуйте, Руслан!
1. Определим стационарные точки, используя необходимые условия экстремума:
Получили одну стационарную точку:
2. Исследуем стационарную точку, используя достаточные условия экстремума:
Такими же будут и значения частных производных в стационарной точке, то есть
Поскольку
постольку 
- точка максимума заданной функции.
3. Вычислим значение функции в точке экстремума:
1. Определим стационарные точки, используя необходимые условия экстремума:
Получили одну стационарную точку:
2. Исследуем стационарную точку, используя достаточные условия экстремума:
Такими же будут и значения частных производных в стационарной точке, то есть
Поскольку
постольку - точка максимума заданной функции.3. Вычислим значение функции в точке экстремума:
5
Спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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