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Popular >

extreme f(x)=x^3+6x^2-x-6

Solution

extreme points

f (x) = x^{3} + 6 x^{2} - x - 6

Solution

Maximum (- \frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 44 + 839), Minimum (\frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 44 - 839)

Solution steps

f^{'} (x) = 3 x^{2} + 12 x - 1

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{6 + 39}{3}

into

x^{3} + 6 x^{2} - x - 6 : \frac{- 288 - 46 39}{9} + 44 + 839

Maximum (- \frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 44 + 839)

Plug

x = \frac{- 6 + 39}{3}

into

x^{3} + 6 x^{2} - x - 6 : \frac{46 39 - 288}{9} + 44 - 839

Minimum (\frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 44 - 839)

Maximum (- \frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 44 + 839), Minimum (\frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 44 - 839)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3+6x^2-x-6 ?
The extreme f(x)=x^3+6x^2-x-6 is