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

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

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

extreme points

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

Minimum (- 1, 2), Maximum (1, - 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, 2)

Plug

x = 1

into

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

Maximum (1, - 2)

Minimum (- 1, 2), Maximum (1, - 2)

f (x) = \frac{ln ( x )}{x ^{3}}

f (x) = \frac{x + 9}{x - 9}

x + 4

f (x) = (x + 8)^{3}

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