What is the extreme f(x)= 1/3 x^3-1/2 x^2-6x ?

The extreme f(x)= 1/3 x^3-1/2 x^2-6x is Maximum(-2, 22/3),Minimum(3,-27/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)= 1/3 x^3-1/2 x^2-6x

extreme points

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

Maximum (- 2, \frac{22}{3}), Minimum (3, - \frac{27}{2})

Solution steps

f^{'} (x) = x^{2} - x - 6

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : \frac{22}{3}

Maximum (- 2, \frac{22}{3})

Plug

x = 3

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : - \frac{27}{2}

Minimum (3, - \frac{27}{2})

Maximum (- 2, \frac{22}{3}), Minimum (3, - \frac{27}{2})

What is the extreme f(x)= 1/3 x^3-1/2 x^2-6x ?
The extreme f(x)= 1/3 x^3-1/2 x^2-6x is Maximum(-2, 22/3),Minimum(3,-27/2)