Difference between revisions of "Differentiability"

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Line 7: Line 7:
  
 
<jsxgraph box="box" width="600" height="400">
 
<jsxgraph box="box" width="600" height="400">
//JXG.Options.text.useMathJax = true;
 
 
board = JXG.JSXGraph.initBoard('box', {
 
board = JXG.JSXGraph.initBoard('box', {
 
     boundingbox: [-5, 10, 7, -6],  
 
     boundingbox: [-5, 10, 7, -6],  
Line 34: Line 33:
 
      
 
      
 
var txt = board.create('text', [2, 7, function() {  
 
var txt = board.create('text', [2, 7, function() {  
         return ':<math>\\frac{' +  
+
         return '(' +  
 
               fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +  
 
               fx.Y().toFixed(2) + '-(' + fx0.Y().toFixed(2) +  
               ')}{' +  
+
               '))(' +  
 
               fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +
 
               fx.X().toFixed(2) + '-(' + fx0.X().toFixed(2) +
               ')} = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3) + '</math>';
+
               ')) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);
 
     }]);
 
     }]);
  

Revision as of 20:33, 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]


The underlying JavaScript code