Does it make sense to say that a function is increasing (or decreasing) at a point?
A) Yes, it makes sense, and it is defined as f'(a) > 0 (f'(a) < 0) at that point.
B) No, it doesn't make sense to talk about a function being increasing (or decreasing) at a single point.
C) Yes, it makes sense, and it is defined as f'(a) ≥ 0 (f'(a) ≤ 0) at that point.
D) It depends on the context and the behavior of the function around that point.
