Difference between revisions of "Differentiability"

From JSXGraph Wiki
Jump to: navigation, search
Line 1: Line 1:
If the function <math>f: D \to {\mathbb R}</math> is differentiable in <math>x_0\in D</math>
+
If the function <math>f: D \to 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(x) = f(x_0) + (x-x_0) f_1(x) </math>
 +
 
 
<html>
 
<html>
 
   <script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script>
 
   <script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script>

Revision as of 21:25, 22 January 2019

If the function [math]f: D \to 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(x) = f(x_0) + (x-x_0) f_1(x) [/math]

The underlying JavaScript code