What is the extreme f(x)=3x-36x^{1/3} ?

The extreme f(x)=3x-36x^{1/3} is Minimum(-8,48),Maximum(0,0),Minimum(8,-48)

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extreme f(x)=3x-36x^{1/3}

extreme points

f (x) = 3 x - 36 x^{\frac{1}{3}}

Minimum (- 8, 48), Maximum (0, 0), Minimum (8, - 48)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{8},

Increasing

: - \frac{1}{8} < x < \frac{1}{8},

Decreasing

: \frac{1}{8} < x < \infty

Plug

x = - 8

into

3 x - 36 x^{\frac{1}{3}} : 48

Minimum (- 8, 48)

Plug

x = 0

into

3 x - 36 x^{\frac{1}{3}} : 0

Maximum (0, 0)

Plug

x = 8

into

3 x - 36 x^{\frac{1}{3}} : - 48

Minimum (8, - 48)

Minimum (- 8, 48), Maximum (0, 0), Minimum (8, - 48)

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f (x) = 10 - 5 x

f (x) = - \frac{2}{3} x + \frac{1}{6}

\frac{3 x + 9}{x}

What is the extreme f(x)=3x-36x^{1/3} ?
The extreme f(x)=3x-36x^{1/3} is Minimum(-8,48),Maximum(0,0),Minimum(8,-48)