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Popular >

extreme f(x)=5-2x+3x^2-x^3

Solution

extreme points

f (x) = 5 - 2 x + 3 x^{2} - x^{3}

Solution

Minimum (\frac{3 - 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 9), Maximum (\frac{3 + 3}{3}, 23 + \frac{- 16 - 12 3}{3 3} + 9)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{3} + 1,

Increasing

: - \frac{1}{3} + 1 < x < \frac{1}{3} + 1,

Decreasing

: \frac{1}{3} + 1 < x < \infty

Plug

x = \frac{3 - 3}{3}

into

5 - 2 x + 3 x^{2} - x^{3} : - 23 + \frac{16 - 12 3}{3 3} + 9

Minimum (\frac{3 - 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 9)

Plug

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

into

5 - 2 x + 3 x^{2} - x^{3} : 23 + \frac{- 16 - 12 3}{3 3} + 9

Maximum (\frac{3 + 3}{3}, 23 + \frac{- 16 - 12 3}{3 3} + 9)

Minimum (\frac{3 - 3}{3}, - 23 + \frac{16 - 12 3}{3 3} + 9), Maximum (\frac{3 + 3}{3}, 23 + \frac{- 16 - 12 3}{3 3} + 9)

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Frequently Asked Questions (FAQ)

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