What is the extreme f(x)=2x-24x^{1/3} ?

The extreme f(x)=2x-24x^{1/3} is Minimum(-8,32),Maximum(0,0),Minimum(8,-32)

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extreme f(x)=2x-24x^{1/3}

extreme points

f (x) = 2 x - 24 x^{\frac{1}{3}}

Minimum (- 8, 32), Maximum (0, 0), Minimum (8, - 32)

Solution steps

f^{'} (x) = 2 - \frac{8}{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

2 x - 24 x^{\frac{1}{3}} : 32

Minimum (- 8, 32)

Plug

x = 0

into

2 x - 24 x^{\frac{1}{3}} : 0

Maximum (0, 0)

Plug

x = 8

into

2 x - 24 x^{\frac{1}{3}} : - 32

Minimum (8, - 32)

Minimum (- 8, 32), Maximum (0, 0), Minimum (8, - 32)

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f (x) = 3 x - 5

4 x 4 x^{2} + 2

f (x) = 4 sin^{2} (x) [0, π]

f (x) = 0.028 e^{- \frac{x}{2}}

What is the extreme f(x)=2x-24x^{1/3} ?
The extreme f(x)=2x-24x^{1/3} is Minimum(-8,32),Maximum(0,0),Minimum(8,-32)