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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=(x^3)/(x-2)

extreme

Saddle (0, 0), Minimum (3, 27)

Solution steps

f^{'} (x) = \frac{2 x ^{3} - 6 x ^{2}}{( x - 2 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{3}}{x - 2} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{x ^{3}}{x - 2} : 27

Minimum (3, 27)

Saddle (0, 0), Minimum (3, 27)

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