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Popular >

extreme f(x)=(x-3)(x+1)(x+5)

Solution

extreme points

f (x) = (x - 3) (x + 1) (x + 5)

Solution

Maximum (- \frac{3 + 4}{3}, \frac{128 + 45 3}{3 3} - 15), Minimum (\frac{- 3 + 4 3}{3}, \frac{45 3 - 128}{3 3} - 15)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x - 13

Find intervals:

Increasing

: - \infty < x < - \frac{4}{3} - 1,

Decreasing

: - \frac{4}{3} - 1 < x < \frac{4}{3} - 1,

Increasing

: \frac{4}{3} - 1 < x < \infty

Plug

x = - \frac{3 + 4}{3}

into

(x - 3) (x + 1) (x + 5) : \frac{128 + 45 3}{3 3} - 15

Maximum (- \frac{3 + 4}{3}, \frac{128 + 45 3}{3 3} - 15)

Plug

x = \frac{- 3 + 4 3}{3}

into

(x - 3) (x + 1) (x + 5) : \frac{45 3 - 128}{3 3} - 15

Minimum (\frac{- 3 + 4 3}{3}, \frac{45 3 - 128}{3 3} - 15)

Maximum (- \frac{3 + 4}{3}, \frac{128 + 45 3}{3 3} - 15), Minimum (\frac{- 3 + 4 3}{3}, \frac{45 3 - 128}{3 3} - 15)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x-3)(x+1)(x+5) ?
The extreme f(x)=(x-3)(x+1)(x+5) is