What is the extreme f(x,y)=e^{x^2-y^2} ?

The extreme f(x,y)=e^{x^2-y^2} is Saddle(0,0)

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 2 (- 2 e^{x^{2} - y^{2}} y^{2} + e^{x^{2} - y^{2}})

D (x, y) = - 4 (2 e^{x^{2} - y^{2}} x^{2} + e^{x^{2} - y^{2}}) (- 2 e^{x^{2} - y^{2}} y^{2} + e^{x^{2} - y^{2}}) - 16 e^{2 (x^{2} - y^{2})} x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

x^{3} - 12 x + 2

f (x, y) = \frac{1}{3} y^{3} + x^{2} - 2 x y - 15 y + 12

F (x, y) = y^{3} + 3 x^{2} y - 6 x^{2} - 6 y^{2} + 2

f (x, y) = - x^{2} - 4 y^{2} + 6 x + 32 y - 76

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