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Popular Functions >

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

Solution

extreme points

f (x) = (3 x - 1) (x + 3) (x - 2)

Solution

Maximum (- \frac{2 + 5 7}{9}, 107 + \frac{70 - 680 7}{243} + 10), Minimum (\frac{- 2 + 5 7}{9}, - 107 + \frac{70 + 680 7}{243} + 10)

Solution steps

f^{'} (x) = 9 x^{2} + 4 x - 19

Find intervals:

Increasing

: - \infty < x < \frac{- 5 7 - 2}{9},

Decreasing

: \frac{- 5 7 - 2}{9} < x < \frac{5 7 - 2}{9},

Increasing

: \frac{5 7 - 2}{9} < x < \infty

Plug

x = - \frac{2 + 5 7}{9}

into

(3 x - 1) (x + 3) (x - 2) : 107 + \frac{70 - 680 7}{243} + 10

Maximum (- \frac{2 + 5 7}{9}, 107 + \frac{70 - 680 7}{243} + 10)

Plug

x = \frac{- 2 + 5 7}{9}

into

(3 x - 1) (x + 3) (x - 2) : - 107 + \frac{70 + 680 7}{243} + 10

Minimum (\frac{- 2 + 5 7}{9}, - 107 + \frac{70 + 680 7}{243} + 10)

Maximum (- \frac{2 + 5 7}{9}, 107 + \frac{70 - 680 7}{243} + 10), Minimum (\frac{- 2 + 5 7}{9}, - 107 + \frac{70 + 680 7}{243} + 10)

Graph

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Frequently Asked Questions (FAQ)

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