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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{3 + 2}{3}, 43 + \frac{- 20 - 12 3}{3 3} + 4), Minimum (\frac{- 3 + 2 3}{3}, - 43 + \frac{20 - 12 3}{3 3} + 4)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x - 1

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3} - 1,

Decreasing

: - \frac{2}{3} - 1 < x < \frac{2}{3} - 1,

Increasing

: \frac{2}{3} - 1 < x < \infty

Plug

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

into

x^{3} + 3 x^{2} - x - 3 : 43 + \frac{- 20 - 12 3}{3 3} + 4

Maximum (- \frac{3 + 2}{3}, 43 + \frac{- 20 - 12 3}{3 3} + 4)

Plug

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

into

x^{3} + 3 x^{2} - x - 3 : - 43 + \frac{20 - 12 3}{3 3} + 4

Minimum (\frac{- 3 + 2 3}{3}, - 43 + \frac{20 - 12 3}{3 3} + 4)

Maximum (- \frac{3 + 2}{3}, 43 + \frac{- 20 - 12 3}{3 3} + 4), Minimum (\frac{- 3 + 2 3}{3}, - 43 + \frac{20 - 12 3}{3 3} + 4)

Popular Examples

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extreme f(x)=3x^4+5x+2 extreme points

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3+3x^2-x-3 ?
The extreme f(x)=x^3+3x^2-x-3 is