If a function is continuous at a point, then it is differentiable at that point. which would be false. If a function is differentiable at a point, then it is continuous at that point. which would be true. ted s, the only difference between the statements f has a derivative at x1 and f is differentiable at x1 is the part of speech that the calculus term holds: the former is a noun and the latter is an adjective.