Differentiability: Difference between revisions
From JSXGraph Wiki
A WASSERMANN (talk | contribs) No edit summary |
A WASSERMANN (talk | contribs) No edit summary |
||
| Line 7: | Line 7: | ||
<jsxgraph box="box" width="600" height="400"> | <jsxgraph box="box" width="600" height="400"> | ||
board = JXG.JSXGraph.initBoard('box', { | board = JXG.JSXGraph.initBoard('box', { | ||
boundingbox: [-5, 10, 7, -6], | boundingbox: [-5, 10, 7, -6], | ||
| Line 34: | Line 33: | ||
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 19:33, 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]
