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

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

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

extreme

Maximum (0, 0), Saddle (2, 2), Saddle (- 2, 2)

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(2, 2) :

Saddle

Check critical point

(- 2, 2) :

Saddle

Maximum (0, 0), Saddle (2, 2), Saddle (- 2, 2)

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