What is the extreme f(x,y)=e^x-xe^y ?

The extreme f(x,y)=e^x-xe^y is Saddle(0,0)

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extreme f(x,y)=e^x-xe^y

extreme

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - e^{x + y} x - e^{2 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)=e^x-xe^y ?
The extreme f(x,y)=e^x-xe^y is Saddle(0,0)