What is the extreme f(x,y)=x^2+y-e^{x+y} ?

The extreme f(x,y)=x^2+y-e^{x+y} is Saddle(1/2 ,-1/2)

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

extreme

Saddle (\frac{1}{2}, - \frac{1}{2})

Solution steps

Find the critical points:

(\frac{1}{2}, - \frac{1}{2})

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

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

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, - \frac{1}{2}) :

Saddle

Saddle (\frac{1}{2}, - \frac{1}{2})

What is the extreme f(x,y)=x^2+y-e^{x+y} ?
The extreme f(x,y)=x^2+y-e^{x+y} is Saddle(1/2 ,-1/2)