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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = - 8

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = x^{4} - 2 x^{2} + y^{3} - 27 y - 15

f (x) = 0.01 x^{2} - 0.2 x + 8

f (x) = - 2500 x^{2} + 45000 + 1360000

f (x) = x + 12 x^{2} - 72 x + 3

f (x, y) = 8 x^{2} - x y + 17 x - 17 y - 18

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