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 points

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

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)

f (x) = x^{4} - 2 x^{2} + x - 2

f (x) = x^{2} - 2 x - 9, 0 \leq x \leq 3

f (x) = tan (\frac{π x}{32}), 0 \leq x \leq 8

3 x^{3} + 9 x^{2} + 27 x - 21

f (x, y) = 5 x ln (1 y - 9) + 5 y - 5

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)