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Popular >

extreme f(x)=-3+8x-x^3

Solution

extreme points

f (x) = - 3 + 8 x - x^{3}

Solution

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 3), Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 3)

Solution steps

f^{'} (x) = - 3 x^{2} + 8

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

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

into

- 3 + 8 x - x^{3} : - \frac{32 2}{3 3} - 3

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 3)

Plug

x = \frac{2 2}{3}

into

- 3 + 8 x - x^{3} : \frac{32 2}{3 3} - 3

Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 3)

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 3), Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 3)

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Frequently Asked Questions (FAQ)

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