What is the monotone f(x)=(2x-8)^{2/3} ?

The monotone f(x)=(2x-8)^{2/3} is Decreasing:-infinity <x<4,Increasing:4<x<infinity

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monotone f(x)=(2x-8)^{2/3}

monotone

Decreasing : - \infty < x < 4, Increasing : 4 < x < \infty

Solution steps

f^{'} (x) = \frac{4}{3 ( 2 x - 8 ) ^{\frac{1}{3}}}

Find intervals:

Decreasing

: - \infty < x < 4,

Increasing

: 4 < x < \infty

Decreasing : - \infty < x < 4, Increasing : 4 < x < \infty

What is the monotone f(x)=(2x-8)^{2/3} ?
The monotone f(x)=(2x-8)^{2/3} is Decreasing:-infinity <x<4,Increasing:4<x<infinity