```ad-note title: Theorem A [[Science/Math/Functions/Function|function]] is differentiable over an *open* interval if it is differentiable at every number in that interval, that is, if its [[Derivative|derivative]] is defined at every number in that interval. ``` ```ad-note title: Theorem If a function is differentiable over an interval, then it must also be [[Continuity|continuous]] over that interval. - However, a continuous function need not to be differentiable. ```