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

This question appeared quite recently.  For a function f to have a derivative, it MUST be continuous on the interval of interest.

 

Therefore if you know that f' is continuous, it must be the derivative of a differentiable function f, and that includes, of necessity, the continuity of f (it's a pre-condition).

 

Q.E.D.