What is the extreme f(x)=2x^4-8x^3 ?

The extreme f(x)=2x^4-8x^3 is Saddle(0,0),Minimum(3,-54)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=2x^4-8x^3

extreme points

f (x) = 2 x^{4} - 8 x^{3}

Saddle (0, 0), Minimum (3, - 54)

Solution steps

f^{'} (x) = 8 x^{3} - 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

2 x^{4} - 8 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

2 x^{4} - 8 x^{3} : - 54

Minimum (3, - 54)

Saddle (0, 0), Minimum (3, - 54)

What is the extreme f(x)=2x^4-8x^3 ?
The extreme f(x)=2x^4-8x^3 is Saddle(0,0),Minimum(3,-54)