# Difference between revisions of "Differentiability"

If the function $f: D \to {\mathbb R}$ is differentiable in $x_0\in D$ then there is a function $f_1: D \to {\mathbb R}$ that is continuous in $x_0$ such that
$f(x) = f(x_0) + (x-x_0) f_1(x)$