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Popular Functions >

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

Solution

extreme points

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

Solution

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 4), Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 4 - 43)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 1

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3} + 1,

Decreasing

: - \frac{2}{3} + 1 < x < \frac{2}{3} + 1,

Increasing

: \frac{2}{3} + 1 < x < \infty

Plug

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

into

x^{3} - 3 x^{2} - x + 3 : \frac{12 3 - 20}{3 3} + 43 - 4

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 4)

Plug

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

into

x^{3} - 3 x^{2} - x + 3 : \frac{12 3 + 20}{3 3} - 4 - 43

Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 4 - 43)

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 4), Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 4 - 43)

Graph

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Frequently Asked Questions (FAQ)

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