What is the extreme f(x)=5x-15x^{1/3} ?

The extreme f(x)=5x-15x^{1/3} is Minimum(-1,10),Maximum(1,-10)

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extreme f(x)=5x-15x^{1/3}

extreme points

f (x) = 5 x - 15 x^{\frac{1}{3}}

Minimum (- 1, 10), Maximum (1, - 10)

Solution steps

f^{'} (x) = 5 - \frac{5}{x ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

5 x - 15 x^{\frac{1}{3}} : 10

Minimum (- 1, 10)

Plug

x = 1

into

5 x - 15 x^{\frac{1}{3}} : - 10

Maximum (1, - 10)

Minimum (- 1, 10), Maximum (1, - 10)

\frac{x - 4}{x ^{2} - 16}

f (x) = \frac{- 5 x - 6}{- 15 x - 28}

\frac{1}{x - 2}

\frac{x - 3}{x - 6}

- 3 cos (4 x)

What is the extreme f(x)=5x-15x^{1/3} ?
The extreme f(x)=5x-15x^{1/3} is Minimum(-1,10),Maximum(1,-10)