# Difference between revisions of "Differentiability"

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− | If the function <math>f: D \to R</math> is differentiable in <math>x_0\in D</math> then there is a function | + | If the function <math>f: D \to {\mathbb R}</math> is differentiable in <math>x_0\in D</math> then there is a function |

− | <math>f_1: D \to R</math> that is continuous in <math>x_0</math> such that | + | <math>f_1: D \to {\mathbb R}</math> that is continuous in <math>x_0</math> such that |

:<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math> | :<math> f(x) = f(x_0) + (x-x_0) f_1(x) </math> |

## Revision as of 21:28, 22 January 2019

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

- [math] f(x) = f(x_0) + (x-x_0) f_1(x) [/math]