What is the extreme f(x,y)=xye^{(x+2y)} ?

The extreme f(x,y)=xye^{(x+2y)} is Maximum(-1,-1/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Maximum (- 1, - \frac{1}{2})

Solution steps

Find the critical points:

(- 1, - \frac{1}{2})

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

D (x, y) = x y (e^{x + 2 y} x + 2 e^{x + 2 y}) (4 e^{x + 2 y} y + 4 e^{x + 2 y}) - e^{2 (2 y + x)} (1 + x)^{2} (1 + 2 y)^{2}

Check the sign of at each critical point

Check critical point

(- 1, - \frac{1}{2}) :

Maximum

Maximum (- 1, - \frac{1}{2})

f (x) = x^{3} + y^{3} - 3 x - 3 y

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

f (x) = 5 + 9 x^{2} - 6 x^{3}

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

f (x) = 2 x^{2} + \frac{2048}{x} + 13

What is the extreme f(x,y)=xye^{(x+2y)} ?
The extreme f(x,y)=xye^{(x+2y)} is Maximum(-1,-1/2)