The Weierstrass-Carathéodory criterion for differentiation states that the following are equivalent: * f(x) is differentiable at a. * There exists a function continuous at x0 φ(x) such that f'(x0) = φ(x0) and f(x) = f(x0) + φ(x)(x − x0) as x → x0. * There exists a scalar λ such that f(x) = f(x0) + λ(x − x0) + o(x − x0) as x → x0. File:Límite 01.svg This analysis-related article contains minimal information concerning its topic. You can help the Mathematics Wikia by adding to it.