What is the extreme u(x,y)=y^2e^x+3x^2 ?

The extreme u(x,y)=y^2e^x+3x^2 is Minimum(0,0)

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extreme u(x,y)=y^2e^x+3x^2

extreme points

u (x, y) = y^{2} e^{x} + 3 x^{2}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 2 e^{2 x} y^{2} + 12 e^{x}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = - \frac{2 x}{5 x ^{2} + 8}

f (x) = 2 x^{3} + 6 x - 90 x + 5, - 5 < x < 4

y = 4 x^{2} - 24 x + 1

f (x) = \frac{x ^{4}}{4} - \frac{8 x ^{3}}{3} - 32 x^{2} + 512 x

e^{3 x} (4 - x)

What is the extreme u(x,y)=y^2e^x+3x^2 ?
The extreme u(x,y)=y^2e^x+3x^2 is Minimum(0,0)