What is the extreme f(x)=12x^{2/3}-x ?

The extreme f(x)=12x^{2/3}-x is Minimum(0,0),Maximum(512,256)

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extreme f(x)=12x^{2/3}-x

extreme points

f (x) = 12 x^{\frac{2}{3}} - x

Minimum (0, 0), Maximum (512, 256)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{1}{512},

Increasing

: \frac{1}{512} < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 512

into

12 x^{\frac{2}{3}} - x : 256

Maximum (512, 256)

Minimum (0, 0), Maximum (512, 256)

f (x) = \frac{x ^{2} - x - 6}{x ^{2} - 4}

f (x) = \frac{2 x + 8}{4 x}

f (x) = 6 x - 1 x

f (x) = \frac{2 x + 1}{x ^{2} - 1}

f (x) = \frac{1}{2} x - 9

What is the extreme f(x)=12x^{2/3}-x ?
The extreme f(x)=12x^{2/3}-x is Minimum(0,0),Maximum(512,256)