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

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

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

extreme points

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

Saddle (- 1, 0), Saddle (1, 0)

Solution steps

Find the critical points:

x = - 1, x = 1

Domain of

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug the extreme point

x = - 1

into

\frac{( 1 - x ^{2} ) ^{3}}{x ^{3}} \Rightarrow y = 0

Saddle (- 1, 0)

Plug the extreme point

x = 1

into

\frac{( 1 - x ^{2} ) ^{3}}{x ^{3}} \Rightarrow y = 0

Saddle (1, 0)

Saddle (- 1, 0), Saddle (1, 0)

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