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)

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) = 8 x - \frac{8 x ^{2}}{2} - x y^{2} + \frac{8 y ^{2}}{16} + 7

f (x, y) = x^{2} y + y^{3} - 27 y

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

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

g (x, y) = ln (x + y)

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)