Differentiability: Difference between revisions
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A WASSERMANN (talk | contribs) No edit summary |
A WASSERMANN (talk | contribs) No edit summary |
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<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> | ||
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{ 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', [ | 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 19:35, 22 January 2019
If the function [math]\displaystyle{ f: D \to {\mathbb R} }[/math] is differentiable in [math]\displaystyle{ x_0\in D }[/math] then there is a function [math]\displaystyle{ f_1: D \to {\mathbb R} }[/math] that is continuous in [math]\displaystyle{ x_0 }[/math] such that
- [math]\displaystyle{ f(x) = f(x_0) + (x-x_0) f_1(x) \,. }[/math]
