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

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

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extreme g(x,y)=2x^2-y^2

extreme points

g (x, y) = 2 x^{2} - y^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 8

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 8 x y - 2 x^{4} - 2 y^{4}

f (x) = \frac{x ^{2} \cdot y}{x}

f (x) = 2 x^{3} + 3 x^{2} - 120 x + 4, - 5 \leq x \leq 5

y = 4 (1.5)^{x}

x - 4 - 4

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