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 points

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

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)

f (x, y) = 3 y^{2} + 5 x y + y + x^{2} + 4 x - 5

9

f (x) = \frac{8 - x ^{3}}{x ^{2}}

f (x) = \frac{6 x}{x ^{2} + 25}

f (x) = (x + \frac{1}{x})

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)