What is the extreme f(x)=5x-60x^{1/3} ?

The extreme f(x)=5x-60x^{1/3} is Minimum(-8,80),Maximum(0,0),Minimum(8,-80)

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extreme f(x)=5x-60x^{1/3}

extreme points

f (x) = 5 x - 60 x^{\frac{1}{3}}

Minimum (- 8, 80), Maximum (0, 0), Minimum (8, - 80)

Solution steps

f^{'} (x) = 5 - \frac{20}{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

5 x - 60 x^{\frac{1}{3}} : 80

Minimum (- 8, 80)

Plug

x = 0

into

5 x - 60 x^{\frac{1}{3}} : 0

Maximum (0, 0)

Plug

x = 8

into

5 x - 60 x^{\frac{1}{3}} : - 80

Minimum (8, - 80)

Minimum (- 8, 80), Maximum (0, 0), Minimum (8, - 80)

What is the extreme f(x)=5x-60x^{1/3} ?
The extreme f(x)=5x-60x^{1/3} is Minimum(-8,80),Maximum(0,0),Minimum(8,-80)