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Popular >

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

Solution

extreme points

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

Solution

Maximum (\frac{3 - 3}{3}, - 4 + 23 + \frac{12 3 - 16}{3 3}), Minimum (\frac{3 + 3}{3}, - 4 - 23 + \frac{12 3 + 16}{3 3})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

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

into

x^{3} - 3 x^{2} + 2 x : - 4 + 23 + \frac{12 3 - 16}{3 3}

Maximum (\frac{3 - 3}{3}, - 4 + 23 + \frac{12 3 - 16}{3 3})

Plug

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

into

x^{3} - 3 x^{2} + 2 x : - 4 - 23 + \frac{12 3 + 16}{3 3}

Minimum (\frac{3 + 3}{3}, - 4 - 23 + \frac{12 3 + 16}{3 3})

Maximum (\frac{3 - 3}{3}, - 4 + 23 + \frac{12 3 - 16}{3 3}), Minimum (\frac{3 + 3}{3}, - 4 - 23 + \frac{12 3 + 16}{3 3})

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Frequently Asked Questions (FAQ)

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