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

The extreme f(x)=x-3x^{2/3} is Maximum(0,0),Minimum(8,-4)

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

extreme points

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

Maximum (0, 0), Minimum (8, - 4)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 8

into

x - 3 x^{\frac{2}{3}} : - 4

Minimum (8, - 4)

Maximum (0, 0), Minimum (8, - 4)

f (x) = \frac{x ^{5}}{5} - \frac{8}{3} x^{3}

f (x) = 4 x^{2} - 5 x^{3}

x^{3} - 6 x^{2} + 15

\frac{4 x}{25 - x ^{2}}

f (x) = x^{\frac{1}{5}} (x + 6)

What is the extreme f(x)=x-3x^{2/3} ?
The extreme f(x)=x-3x^{2/3} is Maximum(0,0),Minimum(8,-4)