To know where a function is increasing and decreasing

Let f(x) be a real function defined on I = (a, b) or [a, b) or (a, b] or [a, b]
Suppose f is continuous on I and differentiable in (a, b).
If
(i) f '(c) > 0 ∀ c ∈ (a, b),
then f is strictly increasing on I.
(ii) f '(c) < 0 ∀ c ∈ (a, b),
then f is strictly decreasing on I.
(iii) f '(c) ≥ 0 ∀ c ∈ (a, b),
then f is increasing on I.
(iv) f '(c) ≤ 0 ∀ c ∈ (a, b),
then f is decreasing on I.
(v) f '(c) = 0 ∀ c ∈ (a, b),
then f is constant function.
Note:
Converse of the above statement is not true.
This is because, a function may increase on an interval without having a derivative at one or more points of that interval.