Question

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

Answer 1

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[`