Relationship between Differentiability and Continuity
Theorem:
If a function is differentiable at any point, then it is necessarily continuous at that point; proof of this theorem follows from definitions of differentiability and continuity.
Note: The converse of this theorem is not true.
i.e., continuity is a necessary but not a sufficient condition for the existence of a finite derivative (differentiability).
i.e., differentiability ⇒ continuity
But continuity ⇏ differentiability
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