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Popular >

extreme f(x)=x-8\sqrt[3]{x}

Solution

extreme points

f (x) = x - 8 3 x

Solution

Maximum (- \frac{16 2}{3 3}, \frac{32 2}{3 3}), Minimum (\frac{16 2}{3 3}, - \frac{32 2}{3 3})

Solution steps

f^{'} (x) = 1 - \frac{8}{3 x ^{\frac{2}{3}}}

Find intervals:

Increasing

: - \infty < x < - \frac{16 2}{3 3},

Decreasing

: - \frac{16 2}{3 3} < x < 0,

Decreasing

: 0 < x < \frac{16 2}{3 3},

Increasing

: \frac{16 2}{3 3} < x < \infty

Plug

x = - \frac{16 2}{3 3}

into

x - 8 3 x : \frac{32 2}{3 3}

Maximum (- \frac{16 2}{3 3}, \frac{32 2}{3 3})

Plug

x = \frac{16 2}{3 3}

into

x - 8 3 x : - \frac{32 2}{3 3}

Minimum (\frac{16 2}{3 3}, - \frac{32 2}{3 3})

Maximum (- \frac{16 2}{3 3}, \frac{32 2}{3 3}), Minimum (\frac{16 2}{3 3}, - \frac{32 2}{3 3})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x-8\sqrt[3]{x} ?
The extreme f(x)=x-8\sqrt[3]{x} is