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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

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)

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})

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

Popular Examples

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Frequently Asked Questions (FAQ)

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