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

The monotone (2x^3)/(x^3-1) is Decreasing:-infinity <x<0,Decreasing:0<x<1,Decreasing:1<x<infinity

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

monotone intervals

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

Decreasing : - \infty < x < 0, Decreasing : 0 < x < 1, Decreasing : 1 < x < \infty

Solution steps

Find the critical points:

x = 0

Domain of

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Decreasing : - \infty < x < 0, Decreasing : 0 < x < 1, Decreasing : 1 < x < \infty

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

(5, - 8), (2, 7)

f (x) = ln (e^{x} - 2)

y = - \frac{2}{3} x - 5

f (x) = 2 x + 10

What is the monotone (2x^3)/(x^3-1) ?
The monotone (2x^3)/(x^3-1) is Decreasing:-infinity <x<0,Decreasing:0<x<1,Decreasing:1<x<infinity