What is the extreme ((x^3))/((x-1)^2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme ((x^3))/((x-1)^2)

extreme points

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

Saddle (0, 0), Minimum (3, \frac{27}{4})

Solution steps

f^{'} (x) = \frac{x ^{2} ( x - 3 )}{( x - 1 ) ^{3}}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{3}}{( x - 1 ) ^{2}} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{x ^{3}}{( x - 1 ) ^{2}} : \frac{27}{4}

Minimum (3, \frac{27}{4})

Saddle (0, 0), Minimum (3, \frac{27}{4})

f (x) = x^{\frac{1}{7}} + 3

f (x) = ln (x^{2} + 10 x + 14)

f (x) = - x^{3} + 3 x^{2} + 24 x - 1

g (x) = x 18 - x

5 x^{2} (x - 11) + 3

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