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Popular >

extreme-x^3+8x^2-15x

Solution

extreme points

- x^{3} + 8 x^{2} - 15 x

Solution

Minimum (\frac{8 - 19}{3}, - 5 (8 - 19) + \frac{1024 - 173 19}{27}), Maximum (\frac{8 + 19}{3}, - 5 (8 + 19) + \frac{1024 + 173 19}{27})

Solution steps

f^{'} (x) = - 3 x^{2} + 16 x - 15

Find intervals:

Decreasing

: - \infty < x < \frac{- 19 + 8}{3},

Increasing

: \frac{- 19 + 8}{3} < x < \frac{19 + 8}{3},

Decreasing

: \frac{19 + 8}{3} < x < \infty

Plug

x = \frac{8 - 19}{3}

into

- x^{3} + 8 x^{2} - 15 x : - 5 (8 - 19) + \frac{1024 - 173 19}{27}

Minimum (\frac{8 - 19}{3}, - 5 (8 - 19) + \frac{1024 - 173 19}{27})

Plug

x = \frac{8 + 19}{3}

into

- x^{3} + 8 x^{2} - 15 x : - 5 (8 + 19) + \frac{1024 + 173 19}{27}

Maximum (\frac{8 + 19}{3}, - 5 (8 + 19) + \frac{1024 + 173 19}{27})

Minimum (\frac{8 - 19}{3}, - 5 (8 - 19) + \frac{1024 - 173 19}{27}), Maximum (\frac{8 + 19}{3}, - 5 (8 + 19) + \frac{1024 + 173 19}{27})

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Frequently Asked Questions (FAQ)

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