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

The extreme f(x,y)=y^4-2y^2-x^2-2 is Maximum(0,0),Saddle(0,-1),Saddle(0,1)

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extreme f(x,y)=y^4-2y^2-x^2-2

extreme points

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

Maximum (0, 0), Saddle (0, - 1), Saddle (0, 1)

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y^{2} - 4

D (x, y) = - 2 (12 y^{2} - 4)

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(0, - 1) :

Saddle

Check critical point

(0, 1) :

Saddle

Maximum (0, 0), Saddle (0, - 1), Saddle (0, 1)

What is the extreme f(x,y)=y^4-2y^2-x^2-2 ?
The extreme f(x,y)=y^4-2y^2-x^2-2 is Maximum(0,0),Saddle(0,-1),Saddle(0,1)