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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = e^{x y} x^{2}

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

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

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

f (x, y) = \frac{1}{x ^{2} + y ^{2} + 1}

f (x, y) = x y