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]


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