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Popular >

extreme x^3+3x^2+2x

Solution

extreme points

x^{3} + 3 x^{2} + 2 x

Solution

Maximum (- \frac{3 + 1}{3}, 23 + \frac{- 12 3 - 16}{3 3} + 4), Minimum (\frac{- 3 + 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 4)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{3 + 1}{3}

into

x^{3} + 3 x^{2} + 2 x : 23 + \frac{- 12 3 - 16}{3 3} + 4

Maximum (- \frac{3 + 1}{3}, 23 + \frac{- 12 3 - 16}{3 3} + 4)

Plug

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

into

x^{3} + 3 x^{2} + 2 x : - 23 + \frac{16 - 12 3}{3 3} + 4

Minimum (\frac{- 3 + 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 4)

Maximum (- \frac{3 + 1}{3}, 23 + \frac{- 12 3 - 16}{3 3} + 4), Minimum (\frac{- 3 + 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 4)

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Frequently Asked Questions (FAQ)

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