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Popular >

extreme f(x)=x^4+3x^3-9x^2-23x-12

Solution

extreme points

f (x) = x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12

Solution

Minimum (\frac{- 5 - 393}{8}, \frac{3 ( 131 393 - 4681 )}{512} - 12), Maximum (- 1, 0), Minimum (\frac{- 5 + 393}{8}, - \frac{3 ( 4681 + 131 393 )}{512} - 12)

Solution steps

f^{'} (x) = 4 x^{3} + 9 x^{2} - 18 x - 23

Find intervals:

Decreasing

: - \infty < x < \frac{- 5 - 393}{8},

Increasing

: \frac{- 5 - 393}{8} < x < - 1,

Decreasing

: - 1 < x < \frac{393 - 5}{8},

Increasing

: \frac{393 - 5}{8} < x < \infty

Plug

x = \frac{- 5 - 393}{8}

into

x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12 : \frac{3 ( 131 393 - 4681 )}{512} - 12

Minimum (\frac{- 5 - 393}{8}, \frac{3 ( 131 393 - 4681 )}{512} - 12)

Plug

x = - 1

into

x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12 : 0

Maximum (- 1, 0)

Plug

x = \frac{- 5 + 393}{8}

into

x^{4} + 3 x^{3} - 9 x^{2} - 23 x - 12 : - \frac{3 ( 4681 + 131 393 )}{512} - 12

Minimum (\frac{- 5 + 393}{8}, - \frac{3 ( 4681 + 131 393 )}{512} - 12)

Minimum (\frac{- 5 - 393}{8}, \frac{3 ( 131 393 - 4681 )}{512} - 12), Maximum (- 1, 0), Minimum (\frac{- 5 + 393}{8}, - \frac{3 ( 4681 + 131 393 )}{512} - 12)

Popular Examples

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extreme-8x^3+24x+9 extreme points

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f (x) = x^{3} - 3 x^{2} - 45 x + 25

Frequently Asked Questions (FAQ)

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