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

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

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

extreme points

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

Maximum (- 2, - \frac{27}{4}), Saddle (1, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, - \frac{27}{4})

Plug

x = 1

into

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

Saddle (1, 0)

Maximum (- 2, - \frac{27}{4}), Saddle (1, 0)

f (x) = \frac{2}{x + 3}

f (x) = - \frac{11}{( 5 + x ) ^{2}}

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

f (x) = - 3 (x + 2)

f (x) = \frac{x}{x + 1}

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