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)

f (x, y) = x^{3}

f (x) = x^{2}, - 1 \leq x \leq 2

f (x) = 3 y^{2} + 8 y

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

f (x) = \frac{1}{2} x - sin (x)

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)