...X • ^ ' X We now show that differentiability is a stronger condition than continuity. Lemma 4.1. If f is differentiable at x, then f is continuous at x. Proof. As h — > 0, we have Thus /(x + /i) -> /(x) as h -> 0. NOTE. The converse of Lemma 4.1 is false,...
If f is differentiable at x, then f is continuous at x. PROOF. 