What is the extreme f(x)=9x^{2/3}+3x-6 ?

The extreme f(x)=9x^{2/3}+3x-6 is Minimum(-8,6),Maximum(0,-6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=9x^{2/3}+3x-6

extreme points

f (x) = 9 x^{\frac{2}{3}} + 3 x - 6

Minimum (- 8, 6), Maximum (0, - 6)

Solution steps

f^{'} (x) = \frac{6}{x ^{\frac{1}{3}}} + 3

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{8},

Increasing

: - \frac{1}{8} < x < \infty

Plug

x = - 8

into

9 x^{\frac{2}{3}} + 3 x - 6 : 6

Minimum (- 8, 6)

Plug

x = 0

into

9 x^{\frac{2}{3}} + 3 x - 6 : - 6

Maximum (0, - 6)

Minimum (- 8, 6), Maximum (0, - 6)

What is the extreme f(x)=9x^{2/3}+3x-6 ?
The extreme f(x)=9x^{2/3}+3x-6 is Minimum(-8,6),Maximum(0,-6)