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Popular >

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

Solution

extreme points

f (x) = x (x + 1)^{2} (x - 3)

Solution

Minimum (- 1, 0), Maximum (\frac{7 - 97}{8}, \frac{485 97 - 4523}{512}), Minimum (\frac{7 + 97}{8}, - \frac{485 97 + 4523}{512})

Solution steps

f^{'} (x) = (x + 1) (4 x^{2} - 7 x - 3)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \frac{7 - 97}{8},

Decreasing

: \frac{7 - 97}{8} < x < \frac{7 + 97}{8},

Increasing

: \frac{7 + 97}{8} < x < \infty

Plug

x = - 1

into

x (x + 1)^{2} (x - 3) : 0

Minimum (- 1, 0)

Plug

x = \frac{7 - 97}{8}

into

x (x + 1)^{2} (x - 3) : \frac{485 97 - 4523}{512}

Maximum (\frac{7 - 97}{8}, \frac{485 97 - 4523}{512})

Plug

x = \frac{7 + 97}{8}

into

x (x + 1)^{2} (x - 3) : - \frac{485 97 + 4523}{512}

Minimum (\frac{7 + 97}{8}, - \frac{485 97 + 4523}{512})

Minimum (- 1, 0), Maximum (\frac{7 - 97}{8}, \frac{485 97 - 4523}{512}), Minimum (\frac{7 + 97}{8}, - \frac{485 97 + 4523}{512})

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f (x) = 12 y - 64

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Frequently Asked Questions (FAQ)

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