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

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

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

extreme points

f (x, y) = e^{x y} + 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 - 2 e^{x y} x y - e^{2 x y} - 2 e^{x y} - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 13

f (x) = x^{3} + x^{2} - x - 1

f (x) = (x^{2} + 10) (9 - x^{2})

\frac{2 x}{x ^{2} - 4}

f (x, y) = 3 x^{4} + 3 y^{4} - x y

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