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

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

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

extreme points

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

Saddle (- 1, 0)

Solution steps

Find the critical points:

(- 1, 0)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(- 1, 0) :

Saddle

Saddle (- 1, 0)

f (x) = x^{4} - 108 x

f (x, y) = 11 x^{2} - 2 x y + 2 y^{2} + 3

y = \frac{2 e ^{3 x}}{- 3 x - 1}

f (x) = 6 x^{4} + 11 x^{3} - x^{2} + x

f (x) = - 25 x^{2} - 20 y^{2} + 300 x + 480 y + 200

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