I was watching [the tutorial](https://www.youtube.com/watch?v=Dyl7jPlJXOM). When I differentiated that function (which I wrote in question). I got
$$f'(x)=3x^2-18x+24$$
When I worked on the equation further. And, put that $f'(x)=0$ than, I got that $x=2,4$.
[![enter image description here][1]][1]
I wrote down intervals then.
$$0\leq x<2$$
$$2<x<4$$
$$4<x\leq6$$
I was putting values (from interval) in function then.
$$f'(x)=3(0)^2-18(0)+24$$
$$=24$$ So, the value is increasing the interval ( $[0,2)$ ) since it is positive value.
$$f'(x)=3(3)^2-18(3)+24$$
$$=-3$$
So, the value is decreasing. I will get positive value for $5$ and $6$. For that reason that is increasing.
[1]: https://i.stack.imgur.com/LjDgd.png
