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Popular >

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)

Popular Examples

domain of 5/9 (x-32)domain

\frac{5}{9} (x - 32)

perpendicular y= x/4-1,(-4,5)perpendicular

y = \frac{x}{4} - 1, (- 4, 5)

distance (-5,6),(-2,3)distance

(- 5, 6), (- 2, 3)

range of y(θ)=3cos(θ+pi)range

y (θ) = 3 cos (θ + π)

periodicity of cos(6x)periodicity

cos (6 x)

Frequently Asked Questions (FAQ)

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