Difference between revisions of "Differentiability"

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var txt = board.create('text', [2, 7, function() {  
 
var txt = board.create('text', [2, 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 21:34, 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