If a function is differentiable then it's also continuous. This property is very useful when working with functions, because if we know that a function is differentiable, we immediately know that it's also continuous.

What is the relationship between differentiability and continuity?

A function is differentiable if it has a derivative. You can think of a derivative of a function as its slope. The relationship between continuous functions and differentiability is-- all differentiable functions are continuous but not all continuous functions are differentiable.

Does differentiability always imply continuity?

We see that if a function is differentiable at a point, then it must be continuous at that point. There are connections between continuity and differentiability. Differentiability Implies Continuity If is a differentiable function at , then is continuous at .