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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{5 + 2 13}{3}, \frac{250 + 46 13}{27} + 16 + 613), Minimum (\frac{- 5 + 2 13}{3}, \frac{250 - 46 13}{27} + 16 - 613)

Solution steps

f^{'} (x) = 3 x^{2} + 10 x - 9

Find intervals:

Increasing

: - \infty < x < \frac{- 2 13 - 5}{3},

Decreasing

: \frac{- 2 13 - 5}{3} < x < \frac{2 13 - 5}{3},

Increasing

: \frac{2 13 - 5}{3} < x < \infty

Plug

x = - \frac{5 + 2 13}{3}

into

x^{3} + 5 x^{2} - 9 x + 1 : \frac{250 + 46 13}{27} + 16 + 613

Maximum (- \frac{5 + 2 13}{3}, \frac{250 + 46 13}{27} + 16 + 613)

Plug

x = \frac{- 5 + 2 13}{3}

into

x^{3} + 5 x^{2} - 9 x + 1 : \frac{250 - 46 13}{27} + 16 - 613

Minimum (\frac{- 5 + 2 13}{3}, \frac{250 - 46 13}{27} + 16 - 613)

Maximum (- \frac{5 + 2 13}{3}, \frac{250 + 46 13}{27} + 16 + 613), Minimum (\frac{- 5 + 2 13}{3}, \frac{250 - 46 13}{27} + 16 - 613)

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Frequently Asked Questions (FAQ)

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