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

The extreme f(x)= 1/3 x^3-2x^2 is Maximum(0,0),Minimum(4,-32/3)

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^3-2x^2

extreme points

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

Maximum (0, 0), Minimum (4, - \frac{32}{3})

Solution steps

f^{'} (x) = x^{2} - 4 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

\frac{1}{3} x^{3} - 2 x^{2} : 0

Maximum (0, 0)

Plug

x = 4

into

\frac{1}{3} x^{3} - 2 x^{2} : - \frac{32}{3}

Minimum (4, - \frac{32}{3})

Maximum (0, 0), Minimum (4, - \frac{32}{3})

What is the extreme f(x)= 1/3 x^3-2x^2 ?
The extreme f(x)= 1/3 x^3-2x^2 is Maximum(0,0),Minimum(4,-32/3)