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Popular Functions >

extreme f(x)=x^3+x^2-6x

Solution

extreme points

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

Solution

Maximum (- \frac{1 + 19}{3}, 2 (1 + 19) + \frac{2 - 16 19}{27}), Minimum (\frac{- 1 + 19}{3}, - 2 (19 - 1) + \frac{16 19 + 2}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{- 19 - 1}{3},

Decreasing

: \frac{- 19 - 1}{3} < x < \frac{19 - 1}{3},

Increasing

: \frac{19 - 1}{3} < x < \infty

Plug

x = - \frac{1 + 19}{3}

into

x^{3} + x^{2} - 6 x : 2 (1 + 19) + \frac{2 - 16 19}{27}

Maximum (- \frac{1 + 19}{3}, 2 (1 + 19) + \frac{2 - 16 19}{27})

Plug

x = \frac{- 1 + 19}{3}

into

x^{3} + x^{2} - 6 x : - 2 (19 - 1) + \frac{16 19 + 2}{27}

Minimum (\frac{- 1 + 19}{3}, - 2 (19 - 1) + \frac{16 19 + 2}{27})

Maximum (- \frac{1 + 19}{3}, 2 (1 + 19) + \frac{2 - 16 19}{27}), Minimum (\frac{- 1 + 19}{3}, - 2 (19 - 1) + \frac{16 19 + 2}{27})

Graph

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Frequently Asked Questions (FAQ)

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