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Консультация № 198388
26.04.2020, 08:55
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Исследовать на экстремум функцию z=x²+y³-3xy.
Исследовать на экстремум функцию z=x²+y³-3xy.
Обсуждение
30.04.2020, 02:41
общий
Адресаты:
Я много часов старался отвечать на Ваши консультации. Однако от Вас ни Оценки, ни Спасибо за мои ответы в rfpro.ru/question/198368 и rfpro.ru/question/198382 .
В Вашей учётке "Последнее посещение: 27.04.2020… (2 сут. 08 час… назад) . Я подозреваю, Вам стали не нужны Ответы, и Вы ушли.
Я тоже ухожу с Ваших страниц успеть помочь тем, кто ещё ждёт помощи.
В Вашей учётке "Последнее посещение: 27.04.2020… (2 сут. 08 час… назад) . Я подозреваю, Вам стали не нужны Ответы, и Вы ушли.
Я тоже ухожу с Ваших страниц успеть помочь тем, кто ещё ждёт помощи.
01.05.2020, 05:29
общий
это ответ
Здравствуйте, master87!
В общем случае необходимое и достаточное условие существования экстремума (максимума или минимума) функции двух переменных z(x, y) в некоторой точке имеет вид:
При этом, если производные
положительны, это будет точка минимума, а если отрицательны - точка максимума.
Для функции z = x[sup]2[/sup] + y[sup]3[/sup] - 3xy имеем
Из условия равенства нулю первых производных
определяем множество так называемых стационарных точек (в которых может быть экстремум функции). Оно состоит из точек (0, 0) и (9/4, 3/2). Значение выражения
для этих точек будет равно соответственно -9 и 9, то есть (1, 1/2) - точка локального экстремума (минимума, с учётом положительности вторых производных в этой точке), а точка (0, 0) не является точкой экстремума.
В общем случае необходимое и достаточное условие существования экстремума (максимума или минимума) функции двух переменных z(x, y) в некоторой точке имеет вид:
При этом, если производные
положительны, это будет точка минимума, а если отрицательны - точка максимума.
Для функции z = x[sup]2[/sup] + y[sup]3[/sup] - 3xy имеем
Из условия равенства нулю первых производных
определяем множество так называемых стационарных точек (в которых может быть экстремум функции). Оно состоит из точек (0, 0) и (9/4, 3/2). Значение выражения
для этих точек будет равно соответственно -9 и 9, то есть (1, 1/2) - точка локального экстремума (минимума, с учётом положительности вторых производных в этой точке), а точка (0, 0) не является точкой экстремума.
5
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