Proving continuity of a differentiable function.

Question

Hi

 

I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)?

 

Thanks.

Answer 1

Notice that one of the requirements (conditions) for a function to be differentiable on an interval is that it be continuous on the interval. That is, differentiability on (a,b) could not occur unless f were continuous on (a,b).