Differentiability: Difference between revisions
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var txt = board.create('text', [2, 7, function() { | var txt = board.create('text', [2, 7, function() { | ||
return '<math> | return ':<math>\\frac{' + | ||
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) + '</math>'; | ||
}]); | }]); | ||
Revision as of 19:32, 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]
