What is the extreme f(x)=12x^3-x^4=x^3(12-x) ?

The extreme f(x)=12x^3-x^4=x^3(12-x) is Saddle(0,0),Maximum(9,2187)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=12x^3-x^4=x^3(12-x)

extreme

Saddle (0, 0), Maximum (9, 2187)

Solution steps

f^{'} (x) = x^{2} (3 (12 - x) - x)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = 0

into

x^{3} (12 - x) : 0

Saddle (0, 0)

Plug

x = 9

into

x^{3} (12 - x) : 2187

Maximum (9, 2187)

Saddle (0, 0), Maximum (9, 2187)

What is the extreme f(x)=12x^3-x^4=x^3(12-x) ?
The extreme f(x)=12x^3-x^4=x^3(12-x) is Saddle(0,0),Maximum(9,2187)