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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 2 e^{2 x y} x^{3} y^{3} - 7 e^{2 x y} x^{2} y^{2} - 6 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)

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