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.

This theorem is often written as its contrapositive:

If is not continuous at , then is not differentiable at .

Thus from the theorem above, we see that all differentiable functions on are continuous on . Nevertheless there are continuous functions on that are not differentiable on .

Which of the following functions are continuous but not differentiable on ?
Can we tell from its graph whether the function is differentiable or not at a point ?
What does the graph of a function possibly look like when is not differentiable at ?