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Popular >

extreme-x^3+2x^2+3x

Solution

extreme points

- x^{3} + 2 x^{2} + 3 x

Solution

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

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 : 2 - 13 + \frac{16 + 13}{27}

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

Plug

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

into

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

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

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

Graph

Popular Examples

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f (1) = \frac{2}{3} x^{3} - 4 x^{2} + 6 x + 2

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

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extreme f(x)=8x^3-3xy+y^3 extreme points

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Frequently Asked Questions (FAQ)

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