What is the extreme 5x^{2/3}-x^{1/3} ?

The extreme 5x^{2/3}-x^{1/3} is Minimum(1/1000 ,-1/20)

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extreme 5x^{2/3}-x^{1/3}

extreme

Minimum (\frac{1}{1000}, - \frac{1}{20})

Solution steps

f^{'} (x) = \frac{10}{3 x ^{\frac{1}{3}}} - \frac{1}{3 x ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{1000},

Increasing

: \frac{1}{1000} < x < \infty

Plug

x = \frac{1}{1000}

into

5 x^{\frac{2}{3}} - x^{\frac{1}{3}} : - \frac{1}{20}

Minimum (\frac{1}{1000}, - \frac{1}{20})

What is the extreme 5x^{2/3}-x^{1/3} ?
The extreme 5x^{2/3}-x^{1/3} is Minimum(1/1000 ,-1/20)