How do you solve #x(4-x)(x-6)<=0#?

1 Answer
Nov 19, 2016

Answer:

The answer is #x in [0,4] uu [6,+ oo[#

Explanation:

Let #f(x)=x(4-x)(x-6)#

Let's do a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##0##color(white)(aaaaa)##4##color(white)(aaaaaa)##6##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##x##color(white)(aaaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##4-x##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##-#

#color(white)(aaaa)##x-6##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##-#

For #f(x)<=0#

The solution is #x in [0,4] uu [6,+ oo[#
graph{x(4-x)(x-6) [-14.56, 13.9, -8.47, 5.77]}