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

The extreme f(x)=x^4-4x^3+4 is Saddle(0,4),Minimum(3,-23)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

f (x) = x^{4} - 4 x^{3} + 4

Saddle (0, 4), Minimum (3, - 23)

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} + 4 : 4

Saddle (0, 4)

Plug

x = 3

into

x^{4} - 4 x^{3} + 4 : - 23

Minimum (3, - 23)

Saddle (0, 4), Minimum (3, - 23)

f (x) = - x^{3} + 9 x^{2} - 51

- 3 x

f (x) = (5 - x)^{\frac{1}{3}}

f (x) = y + 5 = 2 (x + 1)

3 (\frac{1}{2})^{x}

What is the extreme f(x)=x^4-4x^3+4 ?
The extreme f(x)=x^4-4x^3+4 is Saddle(0,4),Minimum(3,-23)