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

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

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

extreme points

f (x, y) = 4 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) = - 32

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = (x - 1) (x - 2) (x - 3)

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

f (x) = 3 x^{3} y - 2 x y^{2}

f (x, y) = x^{2} + y^{2} + 4 x - 6 y

f (x, y) = 2 x^{3} + 4 y^{3} + 3 x^{2} - 12 x - 192 y + 5

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