Difference between revisions of "Differentiability"
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<jsxgraph box="box" width="600" height="400"> | <jsxgraph box="box" width="600" height="400"> | ||
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board = JXG.JSXGraph.initBoard('box', { | board = JXG.JSXGraph.initBoard('box', { | ||
boundingbox: [-5, 10, 7, -6], | boundingbox: [-5, 10, 7, -6], | ||
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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); |
}]); | }]); | ||
Revision as of 21:33, 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]
