What is the monotone 3x^{2/3}-x ?

The monotone 3x^{2/3}-x is Decreasing:-infinity <x< 1/8 ,Increasing: 1/8 <x<infinity

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monotone 3x^{2/3}-x

monotone intervals

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

Decreasing : - \infty < x < \frac{1}{8}, Increasing : \frac{1}{8} < x < \infty

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{1}{8},

Increasing

: \frac{1}{8} < x < \infty

Decreasing : - \infty < x < \frac{1}{8}, Increasing : \frac{1}{8} < x < \infty

f (x) = 2 - x

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

f (x) = sin^{2} (2 x)

f (x) = (3 x - 1) (x - 2)^{4}

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

What is the monotone 3x^{2/3}-x ?
The monotone 3x^{2/3}-x is Decreasing:-infinity <x< 1/8 ,Increasing: 1/8 <x<infinity