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January 19, 2017
Posted by **Amy~** on Sunday, September 26, 2010 at 1:14am.

would become x(x^2-3x)

then how would I graph this?

- Math Graphing -
**Reiny**, Sunday, September 26, 2010 at 7:19amx(x^2-3x) < 0

x^2(x-3) < 0

critical values of x=0 , x=3

on a number line, mark x=0 and x=3, splitting the line into 3 parts

1. x<0

pick any number < 0, say x=-5

(+)(-) < 0 , that's what we want

2. 0 < x < 3 , pick a value, let's pick x = 1

(+)(-) < 0 , good !

3. x> 3, let x=5

(+)(+) > 0 , no good

so x < 3 will work.

another way is know what a general cubic looks like

you would have

y = x^2(x-3)

there would be double root at x=0, so it touches at x=0 without crossing, and it crosses at x = 3

easy to sketch, one can see that the curve is below the x-axis for x< 0 as well as between 0 and 3.

so that is our domain, namely x < 3