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

The extreme f(x)=3x^{2/3}-x is Minimum(0,0),Maximum(8,4)

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

extreme points

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

Minimum (0, 0), Maximum (8, 4)

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

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 8

into

3 x^{\frac{2}{3}} - x : 4

Maximum (8, 4)

Minimum (0, 0), Maximum (8, 4)

What is the extreme f(x)=3x^{2/3}-x ?
The extreme f(x)=3x^{2/3}-x is Minimum(0,0),Maximum(8,4)