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Popular >

extreme f(x)=x^3-3x^2-2x-1

Solution

extreme points

f (x) = x^{3} - 3 x^{2} - 2 x - 1

Solution

Maximum (\frac{3 - 15}{3}, \frac{36 - 8 15}{9} + 215 - 9), Minimum (\frac{3 + 15}{3}, \frac{36 + 8 15}{9} - 9 - 215)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3} + 1,

Decreasing

: - \frac{5}{3} + 1 < x < \frac{5}{3} + 1,

Increasing

: \frac{5}{3} + 1 < x < \infty

Plug

x = \frac{3 - 15}{3}

into

x^{3} - 3 x^{2} - 2 x - 1 : \frac{36 - 8 15}{9} + 215 - 9

Maximum (\frac{3 - 15}{3}, \frac{36 - 8 15}{9} + 215 - 9)

Plug

x = \frac{3 + 15}{3}

into

x^{3} - 3 x^{2} - 2 x - 1 : \frac{36 + 8 15}{9} - 9 - 215

Minimum (\frac{3 + 15}{3}, \frac{36 + 8 15}{9} - 9 - 215)

Maximum (\frac{3 - 15}{3}, \frac{36 - 8 15}{9} + 215 - 9), Minimum (\frac{3 + 15}{3}, \frac{36 + 8 15}{9} - 9 - 215)

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Frequently Asked Questions (FAQ)

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