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Popular >

extreme f(x)=x^3+3x^2-28x

Solution

extreme points

f (x) = x^{3} + 3 x^{2} - 28 x

Solution

Maximum (- \frac{3 + 93}{3}, 2 (17 + 93) + \frac{44 93 - 36}{9}), Minimum (\frac{- 3 + 93}{3}, 2 (17 - 93) + \frac{- 44 93 - 36}{9})

Solution steps

f^{'} (x) = 3 x^{2} + 6 x - 28

Find intervals:

Increasing

: - \infty < x < - \frac{31}{3} - 1,

Decreasing

: - \frac{31}{3} - 1 < x < \frac{31}{3} - 1,

Increasing

: \frac{31}{3} - 1 < x < \infty

Plug

x = - \frac{3 + 93}{3}

into

x^{3} + 3 x^{2} - 28 x : 2 (17 + 93) + \frac{44 93 - 36}{9}

Maximum (- \frac{3 + 93}{3}, 2 (17 + 93) + \frac{44 93 - 36}{9})

Plug

x = \frac{- 3 + 93}{3}

into

x^{3} + 3 x^{2} - 28 x : 2 (17 - 93) + \frac{- 44 93 - 36}{9}

Minimum (\frac{- 3 + 93}{3}, 2 (17 - 93) + \frac{- 44 93 - 36}{9})

Maximum (- \frac{3 + 93}{3}, 2 (17 + 93) + \frac{44 93 - 36}{9}), Minimum (\frac{- 3 + 93}{3}, 2 (17 - 93) + \frac{- 44 93 - 36}{9})

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Frequently Asked Questions (FAQ)

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