Calculus: Increasing/Decreasing, Critical Points & Inflection Points

[sickle]

srry if this post is in the wrong section but i was wondering if there are actually precise and universally agreeable definitions of the following terms of calculus. Different textbooks even give contrary definitions. Any help is appreciated thanks.

increasing/decreasing = strictly increasing/decreasing or rather non-decreasing/non-increasing (does this mean f(x2) >= f(x1) or simply f(x2) > f(x1)?)

critical point = when f(x) is defined and f'(x) = 0 or DNE. But do endpoints of finite closed intervals count as critical points?

inflection point = when graph changes concavity (only happens when f''(x) = DNE or 0), but does f'(x) have to be continuous here as well or not?

 

[Studiot]

1) Let f be defined on some set S so that for each m in S and n in S such that m < n.

If and only if

f(m) [tex]\leq[/tex] f(n)

We say that f is increasing on S.

If strict inequality holds ( no equals allowed) we say that f is strictly increasing.

A function which is either increasing or decreasing is called monotone.
A function which both increasing and decreasing is constant.

2) Yes

3) No