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 20:34, 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]
