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Консультация № 194150
10.12.2018, 18:34
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Здравствуйте! У меня возникли сложности с таким вопросом:
Исследовать функцию z=z(x;y) на экстремум:
z=3xy-x^2-4y^2+4x-6y
Исследовать функцию z=z(x;y) на экстремум:
z=3xy-x^2-4y^2+4x-6y
Обсуждение
13.12.2018, 18:39
общий
это ответ
Здравствуйте, natalia.ru_96!
Область определения заданной функции -- вся плоскость
заданная функция дифференцируема в каждой точке.
Установим стационарные точки, применив теорему о необходимых условиях экстремума.
Значит,
-- стационарная точка.
Исследуем полученную точку, применив теорему о достаточных условиях экстремума. Имеем
Значит, -- точка максимума;
Область определения заданной функции -- вся плоскость
заданная функция дифференцируема в каждой точке.Установим стационарные точки, применив теорему о необходимых условиях экстремума.
Значит,
-- стационарная точка.Исследуем полученную точку, применив теорему о достаточных условиях экстремума. Имеем
Значит,
-- точка максимума;
Об авторе:
Facta loquuntur.
Facta loquuntur.
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