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Popular >

extreme-x^3+3x^2+10x

Solution

extreme points

- x^{3} + 3 x^{2} + 10 x

Solution

Minimum (- \frac{- 3 + 39}{3}, 2 (8 - 39) + \frac{- 8 39 - 36}{9}), Maximum (\frac{3 + 39}{3}, 2 (8 + 39) + \frac{8 39 - 36}{9})

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 10

Find intervals:

Decreasing

: - \infty < x < - \frac{13}{3} + 1,

Increasing

: - \frac{13}{3} + 1 < x < \frac{13}{3} + 1,

Decreasing

: \frac{13}{3} + 1 < x < \infty

Plug

x = - \frac{- 3 + 39}{3}

into

- x^{3} + 3 x^{2} + 10 x : 2 (8 - 39) + \frac{- 8 39 - 36}{9}

Minimum (- \frac{- 3 + 39}{3}, 2 (8 - 39) + \frac{- 8 39 - 36}{9})

Plug

x = \frac{3 + 39}{3}

into

- x^{3} + 3 x^{2} + 10 x : 2 (8 + 39) + \frac{8 39 - 36}{9}

Maximum (\frac{3 + 39}{3}, 2 (8 + 39) + \frac{8 39 - 36}{9})

Minimum (- \frac{- 3 + 39}{3}, 2 (8 - 39) + \frac{- 8 39 - 36}{9}), Maximum (\frac{3 + 39}{3}, 2 (8 + 39) + \frac{8 39 - 36}{9})

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Frequently Asked Questions (FAQ)

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