What is the extreme f(x,y)=x^2+y^2+x^2y+5 ?

The extreme f(x,y)=x^2+y^2+x^2y+5 is Minimum(0,0),Saddle(sqrt(2),-1),Saddle(-sqrt(2),-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)=x^2+y^2+x^2y+5

extreme

Minimum (0, 0), Saddle (2, - 1), Saddle (- 2, - 1)

Solution steps

Find the critical points:

(0, 0), (2, - 1), (- 2, - 1)

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

D (x, y) = 2 (2 y + 2) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(2, - 1) :

Saddle

Check critical point

(- 2, - 1) :

Saddle

Minimum (0, 0), Saddle (2, - 1), Saddle (- 2, - 1)

What is the extreme f(x,y)=x^2+y^2+x^2y+5 ?
The extreme f(x,y)=x^2+y^2+x^2y+5 is Minimum(0,0),Saddle(sqrt(2),-1),Saddle(-sqrt(2),-1)