What is the extreme f(x)=x^3-x,0<= x<= 1 ?

The extreme f(x)=x^3-x,0<= x<= 1 is Maximum(0,0),Minimum(1/(sqrt(3)),-2/(3sqrt(3))),Maximum(1,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x^3-x,0<= x<= 1

extreme points

f (x) = x^{3} - x, 0 \leq x \leq 1

Maximum (0, 0), Minimum (\frac{1}{3}, - \frac{2}{3 3}), Maximum (1, 0)

Solution steps

Find the critical points:

x = 0, x = \frac{1}{3}, x = 1

Domain of

x^{3} - x, 0 \leq x \leq 1 : 0 \leq x \leq 1

Find intervals:

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < 1

Plug the extreme point

x = 0

into

x^{3} - x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = \frac{1}{3}

into

x^{3} - x \Rightarrow y = - \frac{2}{3 3}

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

Plug the extreme point

x = 1

into

x^{3} - x \Rightarrow y = 0

Maximum (1, 0)

Maximum (0, 0), Minimum (\frac{1}{3}, - \frac{2}{3 3}), Maximum (1, 0)

f (x) = - x^{2} + 4 x - 3

f (x) = \frac{( - 2 x + 10 )}{( x - 15 ) ^{11}}

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

f (x, y) = x^{2} - 3 y^{2} + 7

f (x, y) = 20 x y - x^{3} - 10 y^{2}

What is the extreme f(x)=x^3-x,0<= x<= 1 ?
The extreme f(x)=x^3-x,0<= x<= 1 is Maximum(0,0),Minimum(1/(sqrt(3)),-2/(3sqrt(3))),Maximum(1,0)