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Popular Functions >

extreme f(x)=x^3-2x^2-6x+1

Solution

extreme

Solution

Maximum (\frac{2 - 22}{3}, \frac{- 16 - 10 22}{27} + 222 - 3), Minimum (\frac{2 + 22}{3}, \frac{10 22 - 16}{27} - 3 - 222)

Solution steps

f^{'} (x) = 3 x^{2} - 4 x - 6

Find intervals:

Increasing

: - \infty < x < \frac{- 22 + 2}{3},

Decreasing

: \frac{- 22 + 2}{3} < x < \frac{22 + 2}{3},

Increasing

: \frac{22 + 2}{3} < x < \infty

Plug

x = \frac{2 - 22}{3}

into

x^{3} - 2 x^{2} - 6 x + 1 : \frac{- 16 - 10 22}{27} + 222 - 3

Maximum (\frac{2 - 22}{3}, \frac{- 16 - 10 22}{27} + 222 - 3)

Plug

x = \frac{2 + 22}{3}

into

x^{3} - 2 x^{2} - 6 x + 1 : \frac{10 22 - 16}{27} - 3 - 222

Minimum (\frac{2 + 22}{3}, \frac{10 22 - 16}{27} - 3 - 222)

Maximum (\frac{2 - 22}{3}, \frac{- 16 - 10 22}{27} + 222 - 3), Minimum (\frac{2 + 22}{3}, \frac{10 22 - 16}{27} - 3 - 222)

Graph

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Frequently Asked Questions (FAQ)

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