What is the extreme g(x)= 1/9 x^9-x ?

The extreme g(x)= 1/9 x^9-x is Maximum(-1, 8/9),Minimum(1,-8/9)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme g(x)= 1/9 x^9-x

extreme

Maximum (- 1, \frac{8}{9}), Minimum (1, - \frac{8}{9})

Solution steps

f^{'} (x) = x^{8} - 1

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{1}{9} x^{9} - x : \frac{8}{9}

Maximum (- 1, \frac{8}{9})

Plug

x = 1

into

\frac{1}{9} x^{9} - x : - \frac{8}{9}

Minimum (1, - \frac{8}{9})

Maximum (- 1, \frac{8}{9}), Minimum (1, - \frac{8}{9})

What is the extreme g(x)= 1/9 x^9-x ?
The extreme g(x)= 1/9 x^9-x is Maximum(-1, 8/9),Minimum(1,-8/9)