What is the extreme f(x)=9x^{2/3}-x ?

The extreme f(x)=9x^{2/3}-x is Minimum(0,0),Maximum(216,108)

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extreme f(x)=9x^{2/3}-x

extreme

Minimum (0, 0), Maximum (216, 108)

Solution steps

f^{'} (x) = \frac{6}{x ^{\frac{1}{3}}} - 1

Find intervals:

Decreasing

: - \infty < x < \frac{1}{216},

Increasing

: \frac{1}{216} < x < \infty

Plug

x = 0

into

9 x^{\frac{2}{3}} - x : 0

Minimum (0, 0)

Plug

x = 216

into

9 x^{\frac{2}{3}} - x : 108

Maximum (216, 108)

Minimum (0, 0), Maximum (216, 108)

What is the extreme f(x)=9x^{2/3}-x ?
The extreme f(x)=9x^{2/3}-x is Minimum(0,0),Maximum(216,108)