What is the extreme f(x)=4x^{1/3}-x^{4/3} ?

The extreme f(x)=4x^{1/3}-x^{4/3} is Maximum(1,3)

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

extreme points

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

Maximum (1, 3)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 1

into

4 x^{\frac{1}{3}} - x^{\frac{4}{3}} : 3

Maximum (1, 3)

What is the extreme f(x)=4x^{1/3}-x^{4/3} ?
The extreme f(x)=4x^{1/3}-x^{4/3} is Maximum(1,3)