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

The extreme f(x,y)=e^x(x+y^2+2y) is Minimum(0,-1)

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

extreme

Minimum (0, - 1)

Solution steps

Find the critical points:

(0, - 1)

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

D (x, y) = - 2 e^{2 x} y^{2} - 4 e^{2 x} y + 2 e^{2 x} x

Check the sign of at each critical point

Check critical point

(0, - 1) :

Minimum

Minimum (0, - 1)

What is the extreme f(x,y)=e^x(x+y^2+2y) ?
The extreme f(x,y)=e^x(x+y^2+2y) is Minimum(0,-1)