What is the critical f(x)=3x^3-6x-y^2+y ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

critical f(x)=3x^3-6x-y^2+y

critical points

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

(- \frac{2}{3}, \frac{1}{2}), (\frac{2}{3}, \frac{1}{2})

Solution steps

3 x^{3} - 6 x - y^{2} + y

Find where

\nabla f (x, y)

is equal to zero or undefined

(- \frac{2}{3}, \frac{1}{2}), (\frac{2}{3}, \frac{1}{2})

f (x) = \frac{1}{4} x^{4} - \frac{1}{3} x^{3} - 6 x^{2}

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

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

\frac{4 e ^{4 x}}{3 x - 15}

2 x^{3} - 15 x^{2} + y^{3} + 6 y^{2}

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