1. The problem statement, all variables and given/known data Prove or disprove: Suppose f:[a,b]->R is continuous. If f is diff on interval (a,b) and f'(x) has a limit at b, then f is diff at b. 2. Relevant equations We say that f is differentiable at x0 to mean that there exists a number A such that: f(x)=f(x0)+A(x-x0)+REM where, lim(x->x0) REM(x)/(x-x0) = 0 3. The attempt at a solution We will prove f is diff at b by showing that that there exists a number A so that f(x)=f(b)+A(x-b)+REM so, lim(x->x0) REM(x)/(x-b) = 0 I have gotten good at normal proofs in this course and am very confused on how to build proofs with this diff theorem. I know that this is true, but am confused how to fashion the plan and how to start the proof. How do I establish the existence of an A that satisfies this? Thanks!