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Popular Functions >

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

Solution

extreme

Solution

Maximum (- \frac{7}{3}, - \frac{26 7}{3 3} + 12 + 621), Minimum (\frac{7}{3}, \frac{26 7}{3 3} + 12 - 621)

Solution steps

f^{'} (x) = 2 (3 x^{2} - 7)

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3},

Decreasing

: - \frac{7}{3} < x < \frac{7}{3},

Increasing

: \frac{7}{3} < x < \infty

Plug

x = - \frac{7}{3}

into

2 (x - 1) (x - 2) (x + 3) : - \frac{26 7}{3 3} + 12 + 621

Maximum (- \frac{7}{3}, - \frac{26 7}{3 3} + 12 + 621)

Plug

x = \frac{7}{3}

into

2 (x - 1) (x - 2) (x + 3) : \frac{26 7}{3 3} + 12 - 621

Minimum (\frac{7}{3}, \frac{26 7}{3 3} + 12 - 621)

Maximum (- \frac{7}{3}, - \frac{26 7}{3 3} + 12 + 621), Minimum (\frac{7}{3}, \frac{26 7}{3 3} + 12 - 621)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2(x-1)(x-2)(x+3) ?
The extreme f(x)=2(x-1)(x-2)(x+3) is