What is the extreme f(x,y)=-x^2+y^2+6xy+4x-4y+7 ?

The extreme f(x,y)=-x^2+y^2+6xy+4x-4y+7 is Saddle(4/5 ,-2/5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=-x^2+y^2+6xy+4x-4y+7

extreme points

f (x, y) = - x^{2} + y^{2} + 6 x y + 4 x - 4 y + 7

Saddle (\frac{4}{5}, - \frac{2}{5})

Solution steps

Find the critical points:

(\frac{4}{5}, - \frac{2}{5})

\frac{\partial ^{2} f}{\partial x ^{2}} = 2

D (x, y) = - 40

Check the sign of at each critical point

Check critical point

(\frac{4}{5}, - \frac{2}{5}) :

Saddle

Saddle (\frac{4}{5}, - \frac{2}{5})

f (x) = \frac{x ^{2}}{x ^{2} + 7}

f (x) = \frac{x ^{2} - 10 x + 21}{2 x - 15}

f (x) = - (x^{2} + 2) (x - 2)

f (x, y) = x^{2} - 6 x y + y^{3} - 3

f (x) = (x + 9)^{\frac{2}{3}}

What is the extreme f(x,y)=-x^2+y^2+6xy+4x-4y+7 ?
The extreme f(x,y)=-x^2+y^2+6xy+4x-4y+7 is Saddle(4/5 ,-2/5)