1. The problem statement, all variables and given/known data From the definition of the derivative, prove that, if f(x) is differentiable at x=c, then f(x) is continuous at x=c. 2. Relevant equations f'(c) = lim [f(x)-f(c)]/(x-c) This is the definition for a function to be differentiable at x->c x=c. 3. The attempt at a solution we are required to prove that lim f(x) = f(c) (this is what it means for the function to be continuous x->c lim f(x) - f(c) = 0 x->c This looks alot like the numerator for the definition of differentiable at x=c. From here, i'm lost.