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Popular Functions >

extreme y=4x^3-8x

Solution

extreme points

y = 4 x^{3} - 8 x

Solution

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}), Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Solution steps

f^{'} (x) = 12 x^{2} - 8

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

4 x^{3} - 8 x : - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3})

Plug

x = \frac{2}{3}

into

4 x^{3} - 8 x : 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3}

Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}), Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Graph

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Frequently Asked Questions (FAQ)

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