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

The extreme f(x)=x^4-3x^3+3x^2-x is Minimum(1/4 ,-27/256),Saddle(1,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Minimum (\frac{1}{4}, - \frac{27}{256}), Saddle (1, 0)

Solution steps

f^{'} (x) = 4 x^{3} - 9 x^{2} + 6 x - 1

Find intervals:

Decreasing

: - \infty < x < \frac{1}{4},

Increasing

: \frac{1}{4} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{4}

into

x^{4} - 3 x^{3} + 3 x^{2} - x : - \frac{27}{256}

Minimum (\frac{1}{4}, - \frac{27}{256})

Plug

x = 1

into

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

Saddle (1, 0)

Minimum (\frac{1}{4}, - \frac{27}{256}), Saddle (1, 0)

\frac{x + 5}{2 - x}

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

f (x) = \frac{- 2}{x ^{2} - 9}

f (x) = - x^{4} + 3 x^{3} + 18

f (x, y) = ln (y + x)

What is the extreme f(x)=x^4-3x^3+3x^2-x ?
The extreme f(x)=x^4-3x^3+3x^2-x is Minimum(1/4 ,-27/256),Saddle(1,0)