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Popular >

extreme f(x)=3x^3-x

Solution

extreme points

f (x) = 3 x^{3} - x

Solution

Maximum (- \frac{1}{3}, \frac{2}{9}), Minimum (\frac{1}{3}, - \frac{2}{9})

Solution steps

f^{'} (x) = 9 x^{2} - 1

Find intervals:

Increasing

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

Decreasing

: - \frac{1}{3} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

3 x^{3} - x : \frac{2}{9}

Maximum (- \frac{1}{3}, \frac{2}{9})

Plug

x = \frac{1}{3}

into

3 x^{3} - x : - \frac{2}{9}

Minimum (\frac{1}{3}, - \frac{2}{9})

Maximum (- \frac{1}{3}, \frac{2}{9}), Minimum (\frac{1}{3}, - \frac{2}{9})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=3x^3-x ?
The extreme f(x)=3x^3-x is Maximum(-1/3 , 2/9),Minimum(1/3 ,-2/9)