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Popular Functions >

extreme-x^3+6x^2+x+1

Solution

extreme

Solution

Minimum (- \frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 51 - 839), Maximum (\frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 51 + 839)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

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

into

- x^{3} + 6 x^{2} + x + 1 : \frac{46 39 - 288}{9} + 51 - 839

Minimum (- \frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 51 - 839)

Plug

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

into

- x^{3} + 6 x^{2} + x + 1 : \frac{- 288 - 46 39}{9} + 51 + 839

Maximum (\frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 51 + 839)

Minimum (- \frac{- 6 + 39}{3}, \frac{46 39 - 288}{9} + 51 - 839), Maximum (\frac{6 + 39}{3}, \frac{- 288 - 46 39}{9} + 51 + 839)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme-x^3+6x^2+x+1 ?
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