0 ] but increases on [ 0,∞ ) since we use 0 in both intervals.I prefer not to use the brackets as long as I have already described the critical points. The main thing is to give the reader enough information to understand the function.-Whenever we use [ this in place of ( , means the extreme value is considered,......
It is true that the interval x<0 is decreasing, because if you pick any two distinct points in the interval a left point and a right point. The right point is always under the left point. However this is true if you include x=0 too. This is because x=0 is a critical point. It is the minimum and is lower than any point to the left of it. By definition the interval (-infinity, 0] is decreasing too.
So, both ways are correct.
Aesthetically, it might seem awkward to say that f(x) decreases on ( -∞ ,0 ] but increases on [ 0,∞ ) since we use 0 in both intervals.
I prefer not to use the brackets as long as I have already described the critical points. The main thing is to give the reader enough information to understand the function.
Whenever we use [ this in place of ( , means the extreme value is considered, with [∞ it willmeanthere is extreme value but by definition ∞ cannot have any extreme value.
Interval notation is just to state/list the members. It is not linked with calculus derivative. I think so.
