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Задать вопрос экспертам

Консультация № 185219

19.01.2012, 19:36

0.00 руб.

0 3 1

Образование

Здравствуйте! У меня возникли сложности с таким вопросом:
Найти точки экстремума данной функции:

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

19.01.2012, 19:51

общий

это ответ

Здравствуйте, Стас!
z_x=3x²+3y
z_y=3y²+3x
Находим стационарные точки
z_x=0
z_y=0
x²+y=0
y²+x=0
y=-x², x⁴+x=0, x=0 (y=0), x=-1 (y=-1).
Исследуем на экстремум
z_xx=6x
z_xy=3
z_yy=6y
1) (0;0)
z_xx*z_yy-z_xy²=0*0-9<0 ---> экстремума нет
1) (-1;-1)
z_xx*z_yy-z_xy²=(-6)*(-6)-9=27>0
z_xx=-6<0
это условие наличия максимума

Ответ: (-1;-1) - точка максимума

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18345

19.01.2012, 20:02

общий

Адресаты:

Здравствуйте, Дмитрий Германович!

Укажите, пожалуйста, что Вы брали производные от функции (отсутствуют знаки "штрих").

С уважением.

Об авторе:
Facta loquuntur.

давно

Влад Кет

Посетитель
340516
7

19.01.2012, 22:38

общий

Здравствуйте, Стас

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