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

1 Answer
Dec 24, 2016

Answer:

The answer is #x in ] 0,3 [#

Explanation:

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

Now, we can establish the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##0##color(white)(aaaa)##3##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x##color(white)(aaaaaaaa)##-##color(white)(aaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##3-x##color(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 [#