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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

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

into

- x^{3} + 2 x^{2} + 3 x + 1 : \frac{16 + 13}{27} + 3 - 13

Minimum (- \frac{- 2 + 13}{3}, \frac{16 + 13}{27} + 3 - 13)

Plug

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

into

- x^{3} + 2 x^{2} + 3 x + 1 : 13 + \frac{16 - 13}{27} + 3

Maximum (\frac{2 + 13}{3}, 13 + \frac{16 - 13}{27} + 3)

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

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Frequently Asked Questions (FAQ)

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