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Popular >

extreme f(x)=4x^3-32x

Solution

extreme points

f (x) = 4 x^{3} - 32 x

Solution

Maximum (- \frac{2 2}{3}, \frac{128 2}{3 3}), Minimum (\frac{2 2}{3}, - \frac{128 2}{3 3})

Solution steps

f^{'} (x) = 12 x^{2} - 32

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

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

into

4 x^{3} - 32 x : \frac{128 2}{3 3}

Maximum (- \frac{2 2}{3}, \frac{128 2}{3 3})

Plug

x = \frac{2 2}{3}

into

4 x^{3} - 32 x : - \frac{128 2}{3 3}

Minimum (\frac{2 2}{3}, - \frac{128 2}{3 3})

Maximum (- \frac{2 2}{3}, \frac{128 2}{3 3}), Minimum (\frac{2 2}{3}, - \frac{128 2}{3 3})

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Frequently Asked Questions (FAQ)

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