What is the extreme f(x,y)=x^3-12x-y^2-8y+18 ?

The extreme f(x,y)=x^3-12x-y^2-8y+18 is Maximum(-2,-4),Saddle(2,-4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=x^3-12x-y^2-8y+18

extreme points

f (x, y) = x^{3} - 12 x - y^{2} - 8 y + 18

Maximum (- 2, - 4), Saddle (2, - 4)

Solution steps

Find the critical points:

(- 2, - 4), (2, - 4)

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

D (x, y) = - 12 x

Check the sign of at each critical point

Check critical point

(- 2, - 4) :

Maximum

Check critical point

(2, - 4) :

Saddle

Maximum (- 2, - 4), Saddle (2, - 4)

f (x) = 45 x + y

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 7

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 1

f (x, y) = x y - x^{2} - y^{2} + x + y + 17

f (x) = 50 y^{2} + x^{2} - x^{2} y

What is the extreme f(x,y)=x^3-12x-y^2-8y+18 ?
The extreme f(x,y)=x^3-12x-y^2-8y+18 is Maximum(-2,-4),Saddle(2,-4)