How do you solve 3x-x^2>0 using a sign chart?

1 Answer
Dec 24, 2016

The answer is x in ] 0,3 [

Explanation:

Let f(x)=x(3-x)

Now, we can establish the sign chart

color(white)(aaaa)xcolor(white)(aaaa)-oocolor(white)(aaaa)0color(white)(aaaa)3color(white)(aaaa)+oo

color(white)(aaaa)xcolor(white)(aaaaaaaa)-color(white)(aaa)+color(white)(aaaa)+

color(white)(aaaa)3-xcolor(white)(aaaaa)+color(white)(aaa)+color(white)(aaaa)-

color(white)(aaaa)f(x)color(white)(aaaaaa)-color(white)(aaa)+color(white)(aaaa)-

Therefore,

f(x)>0, when, x in ] 0,3 [