Differentiability

If the function [math]\displaystyle{ f: D \to R }[/math] is differentiable in [math]\displaystyle{ x_0\in D }[/math] then there is a function [math]\displaystyle{ f_1: D \to R }[/math] that is continuous in [math]\displaystyle{ x_0 }[/math] such that

[math]\displaystyle{ f(x) = f(x_0) + (x-x_0) f_1(x) }[/math]