How do you solve #4X^3-12x^2 > 0#?

1 Answer
Feb 14, 2017

Answer:

The solution is # x in ]3, +oo[#

Explanation:

Let's do some factorisation

#4x^3-12x^2>0#

#4x^2(x-3)>0#

Let #f(x)=4x^2(x-3)#

#AA x in RR, x^2>0#

The sign chart is very simple

#color(white)(aaaa)##x##color(white)(aaaaaa)##-oo##color(white)(aaaa)##3##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x-3##color(white)(aaaaaaa)##-##color(white)(aaaa)##+#

Therefore,

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