>Find the intervals on which it is increasing and those on which it is decreasing of the following function. $$f(x)=x^3-9x^2+24x-12,0\leq x\leq 6$$
After differentiating (once) the function I get that $x=2,4$. But, I was getting confusing by reading those description of in some intervals it is increasing in some intervals it is decreasing.
>Here, symbol of $f'(x)$ is $=(-)(-)=+$ (positive) in $0\leq x<2$ interval. that means $f'(x)>0$. Hence, the function is increasing in the interval $0\leq x<2$.
I was confused for symbol/sign. They wrote $(-)(-)=+$ (positive) but, where they found those sign? If I can understand for the interval than, I can understand for other intervals also. That's why I didn't add further information.
I guess most of people may confuse for a single description. So, I am adding further information from book again.
> symbol $f'(x)$ is $=(+)(-)= negative$. That means $f'(x)<0$, hence the function is decreasing in the interval $2<x<4$
