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

The extreme f(x,y)=y^2+2y-2x^2y is Minimum(0,-1),Saddle(1,0),Saddle(-1,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)=y^2+2y-2x^2y

extreme

Minimum (0, - 1), Saddle (1, 0), Saddle (- 1, 0)

Solution steps

Find the critical points:

(0, - 1), (1, 0), (- 1, 0)

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

D (x, y) = - 8 y - 16 x^{2}

Check the sign of at each critical point

Check critical point

(0, - 1) :

Minimum

Check critical point

(1, 0) :

Saddle

Check critical point

(- 1, 0) :

Saddle

Minimum (0, - 1), Saddle (1, 0), Saddle (- 1, 0)

What is the extreme f(x,y)=y^2+2y-2x^2y ?
The extreme f(x,y)=y^2+2y-2x^2y is Minimum(0,-1),Saddle(1,0),Saddle(-1,0)