What is the extreme f(x,y)=4y^2e^y+6x^2 ?

The extreme f(x,y)=4y^2e^y+6x^2 is Minimum(0,0),Saddle(0,-2)

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extreme f(x,y)=4y^2e^y+6x^2

extreme

Minimum (0, 0), Saddle (0, - 2)

Solution steps

Find the critical points:

(0, 0), (0, - 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4 (e^{y} y^{2} + 4 e^{y} y + 2 e^{y})

D (x, y) = 48 (e^{y} y^{2} + 4 e^{y} y + 2 e^{y})

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(0, - 2) :

Saddle

Minimum (0, 0), Saddle (0, - 2)

What is the extreme f(x,y)=4y^2e^y+6x^2 ?
The extreme f(x,y)=4y^2e^y+6x^2 is Minimum(0,0),Saddle(0,-2)