In this video I go over the theorem: If a function is differentiable then it is also continuous. This theorem basically means if the derivative exists at a, then it is also continuous at a. I also provide a simple proof using the definition of a derivative.

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If a function is differentiable it is continuous: Proof

Theorem

If f is differentiable at a, then f is continuous at a.

Proof

Note: The converse (or opposite) is FALSE; that is, there are functions that are continuous but not differentiable.