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Popular Functions >

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

Solution

extreme points

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

Solution

Maximum (- \frac{1}{3 3}, - \frac{1}{3 3} + (\frac{1}{3 3})^{\frac{1}{3}}), Minimum (\frac{1}{3 3}, \frac{1}{3 3} - (\frac{1}{3 3})^{\frac{1}{3}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3 \cdot 3 ^{\frac{1}{2}}},

Decreasing

: - \frac{1}{3 \cdot 3 ^{\frac{1}{2}}} < x < 0,

Decreasing

: 0 < x < \frac{1}{3 \cdot 3 ^{\frac{1}{2}}},

Increasing

: \frac{1}{3 \cdot 3 ^{\frac{1}{2}}} < x < \infty

Plug

x = - \frac{1}{3 3}

into

x - x^{\frac{1}{3}} : - \frac{1}{3 3} + (\frac{1}{3 3})^{\frac{1}{3}}

Maximum (- \frac{1}{3 3}, - \frac{1}{3 3} + (\frac{1}{3 3})^{\frac{1}{3}})

Plug

x = \frac{1}{3 3}

into

x - x^{\frac{1}{3}} : \frac{1}{3 3} - (\frac{1}{3 3})^{\frac{1}{3}}

Minimum (\frac{1}{3 3}, \frac{1}{3 3} - (\frac{1}{3 3})^{\frac{1}{3}})

Maximum (- \frac{1}{3 3}, - \frac{1}{3 3} + (\frac{1}{3 3})^{\frac{1}{3}}), Minimum (\frac{1}{3 3}, \frac{1}{3 3} - (\frac{1}{3 3})^{\frac{1}{3}})

Graph

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Frequently Asked Questions (FAQ)

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