**Problem Statement:** Let be a continuous function on such that is differentiable at all points of except possibly at a single point . If exists show that exists and that .

**Proof: ** by definition. Consider: . Applying the definition stated above we get the following:

**Reflection: **The only part of this proof that I’m worried about is the switching the limits. I’m 90% sure this is allowed since we’re given that is continuous.

Advertisements