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Popular >

extreme f(x)=4(x-3)^2(x+1)^5(x-9)

Solution

extreme points

f (x) = 4 (x - 3)^{2} (x + 1)^{5} (x - 9)

Solution

Saddle (- 1, 0), Minimum (\frac{39 - 609}{8}, \frac{250820576832 609 - 6204021829056}{2097152} - 324), Maximum (3, 0), Minimum (\frac{39 + 609}{8}, \frac{- 6204021829056 - 250820576832 609}{2097152} - 324)

Solution steps

f^{'} (x) = 4 (2 (x - 3) (x + 1)^{5} (x - 9) + 2 (x + 1)^{4} (3 x - 22) (x - 3)^{2})

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{39 - 609}{8},

Increasing

: \frac{39 - 609}{8} < x < 3,

Decreasing

: 3 < x < \frac{39 + 609}{8},

Increasing

: \frac{39 + 609}{8} < x < \infty

Plug

x = - 1

into

4 (x - 3)^{2} (x + 1)^{5} (x - 9) : 0

Saddle (- 1, 0)

Plug

x = \frac{39 - 609}{8}

into

4 (x - 3)^{2} (x + 1)^{5} (x - 9) : \frac{250820576832 609 - 6204021829056}{2097152} - 324

Minimum (\frac{39 - 609}{8}, \frac{250820576832 609 - 6204021829056}{2097152} - 324)

Plug

x = 3

into

4 (x - 3)^{2} (x + 1)^{5} (x - 9) : 0

Maximum (3, 0)

Plug

x = \frac{39 + 609}{8}

into

4 (x - 3)^{2} (x + 1)^{5} (x - 9) : \frac{- 6204021829056 - 250820576832 609}{2097152} - 324

Minimum (\frac{39 + 609}{8}, \frac{- 6204021829056 - 250820576832 609}{2097152} - 324)

Saddle (- 1, 0), Minimum (\frac{39 - 609}{8}, \frac{250820576832 609 - 6204021829056}{2097152} - 324), Maximum (3, 0), Minimum (\frac{39 + 609}{8}, \frac{- 6204021829056 - 250820576832 609}{2097152} - 324)

Graph

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Frequently Asked Questions (FAQ)

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