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Popular >

extreme x^3-3x^2-23x+8

Solution

extreme points

x^{3} - 3 x^{2} - 23 x + 8

Solution

Maximum (\frac{3 - 78}{3}, \frac{36 + 34 78}{9} + 278 - 21), Minimum (\frac{3 + 78}{3}, \frac{36 - 34 78}{9} - 21 - 278)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 23

Find intervals:

Increasing

: - \infty < x < - \frac{26}{3} + 1,

Decreasing

: - \frac{26}{3} + 1 < x < \frac{26}{3} + 1,

Increasing

: \frac{26}{3} + 1 < x < \infty

Plug

x = \frac{3 - 78}{3}

into

x^{3} - 3 x^{2} - 23 x + 8 : \frac{36 + 34 78}{9} + 278 - 21

Maximum (\frac{3 - 78}{3}, \frac{36 + 34 78}{9} + 278 - 21)

Plug

x = \frac{3 + 78}{3}

into

x^{3} - 3 x^{2} - 23 x + 8 : \frac{36 - 34 78}{9} - 21 - 278

Minimum (\frac{3 + 78}{3}, \frac{36 - 34 78}{9} - 21 - 278)

Maximum (\frac{3 - 78}{3}, \frac{36 + 34 78}{9} + 278 - 21), Minimum (\frac{3 + 78}{3}, \frac{36 - 34 78}{9} - 21 - 278)

Graph

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Frequently Asked Questions (FAQ)

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