What is the critical f(x,y)= 1/3 x^3+y^3+2x^2-12x-3y ?

The critical f(x,y)= 1/3 x^3+y^3+2x^2-12x-3y is (2,1),(2,-1),(-6,1),(-6,-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

critical f(x,y)= 1/3 x^3+y^3+2x^2-12x-3y

critical points

f (x, y) = \frac{1}{3} x^{3} + y^{3} + 2 x^{2} - 12 x - 3 y

(2, 1), (2, - 1), (- 6, 1), (- 6, - 1)

Solution steps

\frac{1}{3} x^{3} + y^{3} + 2 x^{2} - 12 x - 3 y

Find where

\nabla f (x, y)

is equal to zero or undefined

(2, 1), (2, - 1), (- 6, 1), (- 6, - 1)

f (x, y) = 4 x^{2} - 12 x + y^{2} + 2 y - 10

\frac{x}{( x - 1 ) ^{2}}

f (x) = \frac{( x ^{2} + 1 )}{2 x}

y = - \frac{cos ( 2 x )}{2} - 2 sin (x)

y = (2 e^{x}) (I n^{3} x) + 5 x

What is the critical f(x,y)= 1/3 x^3+y^3+2x^2-12x-3y ?
The critical f(x,y)= 1/3 x^3+y^3+2x^2-12x-3y is (2,1),(2,-1),(-6,1),(-6,-1)