Difference between revisions of "Differentiability"

From JSXGraph Wiki
Jump to: navigation, search
Line 3: Line 3:
 
<math>f_1: D \to {\mathbb 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>
  
  
Line 32: Line 32:
 
         { size: 1, name: 'f_1', color: 'black', fixed: true, trace: true});
 
         { size: 1, name: 'f_1', color: 'black', fixed: true, trace: true});
 
      
 
      
var txt = board.create('text', [2, 7, function() {  
+
var txt = board.create('text', [0.5, 7, function() {  
 
         return '( ' +  
 
         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);
 
               ') ) = ' + ((fx.Y()-fx0.Y())/(fx.X()-fx0.X())).toFixed(3);

Revision as of 21:35, 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