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I. Найти стационарные точки функции и исследовать их на экстремум.
11. z=3x3+2xy2+x2 +4y2
1. Определим стационарные точки, используя необходимые условия экстремума функции двух переменных.
Получили две стационарные точки:
2. Исследуем полученные точки на экстремум, используя достаточные условия экстремума функции двух переменных. Сначала вычислим вторые производные заданной функции:
Исследуем точку Значит, -- точка минимума заданной функции.
Исследуем точку значит, не является точкой экстремума заданной функции.
Об авторе:
Facta loquuntur.
Форма ответа
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stroitel 
Значит, 
-- точка минимума заданной функции.
значит, 
не является точкой экстремума заданной функции.