Differentiability: Difference between revisions
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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 19:28, 22 January 2019
If the function [math]\displaystyle{ f: D \to {\mathbb R} }[/math] is differentiable in [math]\displaystyle{ x_0\in D }[/math] then there is a function [math]\displaystyle{ f_1: D \to {\mathbb 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]
