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Консультация № 176493
04.02.2010, 16:16
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Здравствуйте уважаемые эксперты помогите решить пожалуйста задачку по мат.анализу
Найти локальные экстремумы функции
Найти локальные экстремумы функции
Обсуждение
04.02.2010, 17:27
общий
08.02.2010, 01:03
это ответ
Здравствуйте, Верещака Андрей Павлович.
df/dx=3x2-3y
df/dy=-3y2-3x
{ 3x2-3y=0
-3y2-3x=0
{x2=y
y2=-x
x4=-x
3 2 решения - x=0, y=0, x=-1, y=1, y=-1
Достаточным условием локального экстремума будет D>0=d2f/dx2*d2f/dy2-(d2f/dxy)2
d2f/dx2=6x
d2f/dy2=-6y
d2f/dxy=-3
D=-36xy-9
В точке (0,0) D=-9, экстремума нет
В точке (-1,1) D=27, d2f/dx2= -6, точка максимума.
В точке (-1,-1) D=-45, экстремума нет
df/dx=3x2-3y
df/dy=-3y2-3x
{ 3x2-3y=0
-3y2-3x=0
{x2=y
y2=-x
x4=-x
Достаточным условием локального экстремума будет D>0=d2f/dx2*d2f/dy2-(d2f/dxy)2
d2f/dx2=6x
d2f/dy2=-6y
d2f/dxy=-3
D=-36xy-9
В точке (0,0) D=-9, экстремума нет
В точке (-1,1) D=27, d2f/dx2= -6, точка максимума.
Форма ответа
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