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Popular Functions >

extreme f(x)=x^3-2x-1

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{2}{3}

into

x^{3} - 2 x - 1 : - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} - 1

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

Plug

x = \frac{2}{3}

into

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3-2x-1 ?
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