What is the extreme f(x,y)=1-3x^4-6x^2y+2y^3 ?

The extreme f(x,y)=1-3x^4-6x^2y+2y^3 is Maximum(1,-1),Maximum(-1,-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x,y)=1-3x^4-6x^2y+2y^3

extreme

Maximum (1, - 1), Maximum (- 1, - 1)

Solution steps

Find the critical points:

(1, - 1), (- 1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y

D (x, y) = 12 y (- 36 x^{2} - 12 y) - 144 x^{2}

Check the sign of at each critical point

Check critical point

(1, - 1) :

Maximum

Check critical point

(- 1, - 1) :

Maximum

Maximum (1, - 1), Maximum (- 1, - 1)

What is the extreme f(x,y)=1-3x^4-6x^2y+2y^3 ?
The extreme f(x,y)=1-3x^4-6x^2y+2y^3 is Maximum(1,-1),Maximum(-1,-1)