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Popular Functions >

extreme f(x)=(x-3)(x+1)(x+4)

Solution

extreme

Solution

Maximum (- \frac{2 + 37}{3}, \frac{160 + 47 37}{27} + 37 - 10), Minimum (\frac{- 2 + 37}{3}, \frac{160 - 47 37}{27} - 10 - 37)

Solution steps

f^{'} (x) = 3 x^{2} + 4 x - 11

Find intervals:

Increasing

: - \infty < x < \frac{- 37 - 2}{3},

Decreasing

: \frac{- 37 - 2}{3} < x < \frac{37 - 2}{3},

Increasing

: \frac{37 - 2}{3} < x < \infty

Plug

x = - \frac{2 + 37}{3}

into

(x - 3) (x + 1) (x + 4) : \frac{160 + 47 37}{27} + 37 - 10

Maximum (- \frac{2 + 37}{3}, \frac{160 + 47 37}{27} + 37 - 10)

Plug

x = \frac{- 2 + 37}{3}

into

(x - 3) (x + 1) (x + 4) : \frac{160 - 47 37}{27} - 10 - 37

Minimum (\frac{- 2 + 37}{3}, \frac{160 - 47 37}{27} - 10 - 37)

Maximum (- \frac{2 + 37}{3}, \frac{160 + 47 37}{27} + 37 - 10), Minimum (\frac{- 2 + 37}{3}, \frac{160 - 47 37}{27} - 10 - 37)

Graph

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Frequently Asked Questions (FAQ)

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