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Popular Functions >

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

Solution

extreme points

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

Solution

Maximum (\frac{2 - 13}{3}, \frac{- 16 - 13}{27} + 13 - 4), Minimum (\frac{2 + 13}{3}, \frac{13 - 16}{27} - 4 - 13)

Solution steps

f^{'} (x) = 3 x^{2} - 4 x - 3

Find intervals:

Increasing

: - \infty < x < \frac{- 13 + 2}{3},

Decreasing

: \frac{- 13 + 2}{3} < x < \frac{13 + 2}{3},

Increasing

: \frac{13 + 2}{3} < x < \infty

Plug

x = \frac{2 - 13}{3}

into

x^{3} - 2 x^{2} - 3 x - 2 : \frac{- 16 - 13}{27} + 13 - 4

Maximum (\frac{2 - 13}{3}, \frac{- 16 - 13}{27} + 13 - 4)

Plug

x = \frac{2 + 13}{3}

into

x^{3} - 2 x^{2} - 3 x - 2 : \frac{13 - 16}{27} - 4 - 13

Minimum (\frac{2 + 13}{3}, \frac{13 - 16}{27} - 4 - 13)

Maximum (\frac{2 - 13}{3}, \frac{- 16 - 13}{27} + 13 - 4), Minimum (\frac{2 + 13}{3}, \frac{13 - 16}{27} - 4 - 13)

Graph

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Frequently Asked Questions (FAQ)

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