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Консультация № 177355
19.03.2010, 21:40
35.91 руб.
20.03.2010, 00:46
0
2
2
Здравствуйте уважаемые эксперты.
Исследовать функцию u=f(x,y) на экстремум.
Исследовать функцию u=f(x,y) на экстремум.
Обсуждение
Неизвестный
19.03.2010, 22:44
общий
это ответ
Здравствуйте, sanekvseti.
u'|x =32/x - y^2
u'|y = -2xy + y^2
u'|xx = -32/x^2
u'|xy = -2y
u'|yy = -2x+2y
и т.д.
u'|x =32/x - y^2
u'|y = -2xy + y^2
u'|xx = -32/x^2
u'|xy = -2y
u'|yy = -2x+2y
и т.д.
19.03.2010, 23:00
общий
это ответ
Здравствуйте, sanekvseti.
Находим стационарные точки из системы:
ux=0
uy=0
Имеем
32/x-y2=0
-2xy+y2=0
Из первого уравнения находим x=32/y2 и подставляем во второе ---> y3=64 ---> y=4 ---> x=2.
Следовательно, имеем одну стационарную точку. Для ее исследования вычисляем вторые производные
uxx=-32/x2=-8
uxy=-2y=-8
uyy=-2x+2y=4
Выражение
uxxuyy-uxy2=-32-64<0, что является достаточным условием отсутствия экстремума.
Находим стационарные точки из системы:
ux=0
uy=0
Имеем
32/x-y2=0
-2xy+y2=0
Из первого уравнения находим x=32/y2 и подставляем во второе ---> y3=64 ---> y=4 ---> x=2.
Следовательно, имеем одну стационарную точку. Для ее исследования вычисляем вторые производные
uxx=-32/x2=-8
uxy=-2y=-8
uyy=-2x+2y=4
Выражение
uxxuyy-uxy2=-32-64<0, что является достаточным условием отсутствия экстремума.
Форма ответа
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