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Popular >

extreme-7(x+3)^2(x-1)(x-5)

Solution

extreme points

- 7 (x + 3)^{2} (x - 1) (x - 5)

Solution

Maximum (- 3, 0), Minimum (\frac{3 - 17}{2}, - \frac{175 ( 3 - 17 )}{2} - 26617 + 637), Maximum (\frac{3 + 17}{2}, - \frac{175 ( 3 + 17 )}{2} + 637 + 26617)

Solution steps

f^{'} (x) = - 7 (4 x^{3} - 44 x - 24)

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < \frac{3 - 17}{2},

Increasing

: \frac{3 - 17}{2} < x < \frac{3 + 17}{2},

Decreasing

: \frac{3 + 17}{2} < x < \infty

Plug

x = - 3

into

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

Maximum (- 3, 0)

Plug

x = \frac{3 - 17}{2}

into

- 7 (x + 3)^{2} (x - 1) (x - 5) : - \frac{175 ( 3 - 17 )}{2} - 26617 + 637

Minimum (\frac{3 - 17}{2}, - \frac{175 ( 3 - 17 )}{2} - 26617 + 637)

Plug

x = \frac{3 + 17}{2}

into

- 7 (x + 3)^{2} (x - 1) (x - 5) : - \frac{175 ( 3 + 17 )}{2} + 637 + 26617

Maximum (\frac{3 + 17}{2}, - \frac{175 ( 3 + 17 )}{2} + 637 + 26617)

Maximum (- 3, 0), Minimum (\frac{3 - 17}{2}, - \frac{175 ( 3 - 17 )}{2} - 26617 + 637), Maximum (\frac{3 + 17}{2}, - \frac{175 ( 3 + 17 )}{2} + 637 + 26617)

Popular Examples

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Frequently Asked Questions (FAQ)

What is the extreme-7(x+3)^2(x-1)(x-5) ?
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