What is the extreme f(x)=x^4-4x^3+9 ?

The extreme f(x)=x^4-4x^3+9 is Saddle(0,9),Minimum(3,-18)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^4-4x^3+9

extreme

Saddle (0, 9), Minimum (3, - 18)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

x^{4} - 4 x^{3} + 9 : 9

Saddle (0, 9)

Plug

x = 3

into

x^{4} - 4 x^{3} + 9 : - 18

Minimum (3, - 18)

Saddle (0, 9), Minimum (3, - 18)

What is the extreme f(x)=x^4-4x^3+9 ?
The extreme f(x)=x^4-4x^3+9 is Saddle(0,9),Minimum(3,-18)