What is the extreme f(x)=x-16/3 x^3 ?

The extreme f(x)=x-16/3 x^3 is Minimum(-1/4 ,-1/6),Maximum(1/4 , 1/6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x-16/3 x^3

extreme points

f (x) = x - \frac{16}{3} x^{3}

Minimum (- \frac{1}{4}, - \frac{1}{6}), Maximum (\frac{1}{4}, \frac{1}{6})

Solution steps

f^{'} (x) = 1 - 16 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{4},

Increasing

: - \frac{1}{4} < x < \frac{1}{4},

Decreasing

: \frac{1}{4} < x < \infty

Plug

x = - \frac{1}{4}

into

x - \frac{16}{3} x^{3} : - \frac{1}{6}

Minimum (- \frac{1}{4}, - \frac{1}{6})

Plug

x = \frac{1}{4}

into

x - \frac{16}{3} x^{3} : \frac{1}{6}

Maximum (\frac{1}{4}, \frac{1}{6})

Minimum (- \frac{1}{4}, - \frac{1}{6}), Maximum (\frac{1}{4}, \frac{1}{6})

What is the extreme f(x)=x-16/3 x^3 ?
The extreme f(x)=x-16/3 x^3 is Minimum(-1/4 ,-1/6),Maximum(1/4 , 1/6)