Mean Value Theorem - Revision history

A WASSERMANN at 15:29, 20 February 2013

2013-02-20T15:29:52Z

← Older revision		Revision as of 15:29, 20 February 2013
Line 11:		Line 11:

	var g = function(x) {		var g = function(x) {
	return ~~board~~.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());		return JXG.Math.Numerics.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
	};		};

Line 37:		Line 37:

	var g = function(x) {		var g = function(x) {
	return ~~board~~.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());		return JXG.Math.Numerics.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
	};		};

A WASSERMANN at 15:29, 20 February 2013

2013-02-20T15:29:31Z

← Older revision		Revision as of 15:29, 20 February 2013
Line 15:		Line 15:

	var r = board.create('glider', [		var r = board.create('glider', [
	function() { return ~~board~~.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return JXG.Math.Numerics.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(~~board~~.root(g,(p[0].X()+p[1].X())*0.5)); },		function() { return f(JXG.Math.Numerics.root(g,(p[0].X()+p[1].X())*0.5)); },
	graph], {name:' ',size:4,fixed:true});		graph], {name:' ',size:4,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
Line 41:		Line 41:

	var r = board.create('glider', [		var r = board.create('glider', [
	function() { return ~~board~~.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return JXG.Math.Numerics.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(~~board~~.root(g,(p[0].X()+p[1].X())*0.5)); },		function() { return f(JXG.Math.Numerics.root(g,(p[0].X()+p[1].X())*0.5)); },
	graph], {name:' ',size:4,fixed:true});		graph], {name:' ',size:4,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});

A WASSERMANN at 15:28, 20 February 2013

2013-02-20T15:28:45Z

← Older revision		Revision as of 15:28, 20 February 2013
Line 7:		Line 7:
	p[2] = board.create('point', [-0.5,1], {size:2});		p[2] = board.create('point', [-0.5,1], {size:2});
	p[3] = board.create('point', [3,3], {size:2});		p[3] = board.create('point', [3,3], {size:2});
	var f = ~~board~~.lagrangePolynomial(p);		var f = JXG.Math.Numerics.lagrangePolynomial(p);
	var graph = board.create('functiongraph', [f,-10, 10]);		var graph = board.create('functiongraph', [f,-10, 10]);

Line 33:		Line 33:
	p[2] = board.create('point', [-0.5,1], {size:2});		p[2] = board.create('point', [-0.5,1], {size:2});
	p[3] = board.create('point', [3,3], {size:2});		p[3] = board.create('point', [3,3], {size:2});
	var f = ~~board~~.lagrangePolynomial(p);		var f = JXG.Math.Numerics.lagrangePolynomial(p);
	var graph = board.create('functiongraph', [f,-10, 10]);		var graph = board.create('functiongraph', [f,-10, 10]);

Michael at 09:09, 8 June 2011

2011-06-08T09:09:17Z

← Older revision		Revision as of 09:09, 8 June 2011
Line 17:		Line 17:
	function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },		function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
	graph], {name:' ',~~style~~:6,fixed:true});		graph], {name:' ',size:4,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});
Line 43:		Line 43:
	function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },		function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
	graph], {name:' ',~~style~~:6,fixed:true});		graph], {name:' ',size:4,fixed:true});
	board.create('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});

Michael at 09:08, 8 June 2011

2011-06-08T09:08:42Z

← Older revision		Revision as of 09:08, 8 June 2011
Line 29:		Line 29:
	board.suspendUpdate();		board.suspendUpdate();
	var p = [];		var p = [];
	p[0] = board.create('point', [-1,-2], {~~style~~:4});		p[0] = board.create('point', [-1,-2], {size:2});
	p[1] = board.create('point', [6,5], {~~style~~:4});		p[1] = board.create('point', [6,5], {size:2});
	p[2] = board.create('point', [-0.5,1], {~~style~~:4});		p[2] = board.create('point', [-0.5,1], {size:2});
	p[3] = board.create('point', [3,3], {~~style~~:4});		p[3] = board.create('point', [3,3], {size:2});
	var f = board.lagrangePolynomial(p);		var f = board.lagrangePolynomial(p);
	var graph = board.create('functiongraph', [f,-10, 10]);		var graph = board.create('functiongraph', [f,-10, 10]);

Michael at 09:08, 8 June 2011

2011-06-08T09:08:32Z

← Older revision		Revision as of 09:08, 8 June 2011
Line 1:		Line 1:
	<jsxgraph width="600" height="400" box="box">		<jsxgraph width="600" height="400" box="box">
	var board = JXG.JSXGraph.initBoard('box', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 50~~, ~~unitY: 25~~, axis:true});		var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis:true});
	board.suspendUpdate();		board.suspendUpdate();
	var p = [];		var p = [];
	p[0] = board.create('point', [-1,-2], {~~style~~:4});		p[0] = board.create('point', [-1,-2], {size:2});
	p[1] = board.create('point', [6,5], {~~style~~:4});		p[1] = board.create('point', [6,5], {size:2});
	p[2] = board.create('point', [-0.5,1], {~~style~~:4});		p[2] = board.create('point', [-0.5,1], {size:2});
	p[3] = board.create('point', [3,3], {~~style~~:4});		p[3] = board.create('point', [3,3], {size:2});
	var f = board.lagrangePolynomial(p);		var f = board.lagrangePolynomial(p);
	var graph = board.create('functiongraph', [f,-10, 10]);		var graph = board.create('functiongraph', [f,-10, 10]);
Line 26:		Line 26:
	===The underlying JavaScript code===		===The underlying JavaScript code===
	<source lang="javascript">		<source lang="javascript">
	var board = JXG.JSXGraph.initBoard('box', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 50~~, ~~unitY: 25~~, axis:true});		var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis:true});
	board.suspendUpdate();		board.suspendUpdate();
	var p = [];		var p = [];

A WASSERMANN at 10:25, 25 March 2011

2011-03-25T10:25:23Z

← Older revision		Revision as of 10:25, 25 March 2011
Line 1:		Line 1:
	<~~html>~~		<jsxgraph width="600" height="400" box="box">
	~~<link rel="stylesheet" type="text/css" href="http://~~jsxgraph~~.uni-bayreuth.de/distrib/jsxgraph.css" />~~
	~~<script type~~="~~text/javascript~~" ~~src~~="~~http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js~~"~~></script>~~
	~~<div id~~="box~~" class="jxgbox" style="width:600px; height:400px;"></div>~~
	~~<script language="JavaScript~~">
	var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});		var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
	board.suspendUpdate();		board.suspendUpdate();
Line 26:		Line 22:

	board.unsuspendUpdate();		board.unsuspendUpdate();
	</~~script>~~		</jsxgraph>
	~~</html~~>

	===The underlying JavaScript code===		===The underlying JavaScript code===

A WASSERMANN at 10:24, 27 January 2010

2010-01-27T10:24:42Z

← Older revision		Revision as of 10:24, 27 January 2010
Line 4:		Line 4:
	<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>		<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});		var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
	board.suspendUpdate();		board.suspendUpdate();
	~~// Axes~~		var p = [];
	~~xax~~ = board.~~createElement~~('~~axis~~', [[0,0], [1,0]], {});		p[0] = board.create('point', [-1,-2], {style:4});
	~~yax~~ = board.~~createElement~~('~~axis~~', [[0,0], [0,1]], {});		p[1] = board.create('point', [6,5], {style:4});
			p[2] = board.create('point', [-0.5,1], {style:4});
			p[3] = board.create('point', [3,3], {style:4});
			var f = board.lagrangePolynomial(p);
			var graph = board.create('functiongraph', [f,-10, 10]);

	var p = ~~[];~~		var g = function(x) {
	~~p[0] =~~ board.~~createElement~~(~~'point', [~~-~~1,-2], {style:4});~~		return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
	p[1] ~~= board~~.~~createElement~~(~~'point', [6,5], {style:4}~~);		};
	p[2] ~~= board~~.~~createElement~~(~~'point',~~ [~~-0.5,~~1]~~, {style:4}~~);
	p[3] ~~= board~~.~~createElement~~(~~'point', [3,3], {style:4}~~);
	~~var f = board.lagrangePolynomial(p~~);
	~~var graph = board.createElement('functiongraph', [f,-10, 10])~~;

	~~var g = function(x) {~~		var r = board.create('glider', [
	~~return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());~~
	}

	var r = board.~~createElement~~('glider', [
	function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },		function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.~~createElement~~('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	line = board.~~createElement~~('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});

	board.unsuspendUpdate();		board.unsuspendUpdate();
Line 35:		Line 31:
	===The underlying JavaScript code===		===The underlying JavaScript code===
	<source lang="javascript">		<source lang="javascript">
	board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});		var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
	board.suspendUpdate();		board.suspendUpdate();
	~~// Axes~~		var p = [];
	~~xax = board.createElement('axis', [[0,0], [1,0]], {});~~		p[0] = board.create('point', [-1,-2], {style:4});
	~~yax = board.createElement('axis', [[0,0], [0,1]], {});~~		p[1] = board.create('point', [6,5], {style:4});
			p[2] = board.create('point', [-0.5,1], {style:4});
	var p = [];		p[3] = board.create('point', [3,3], {style:4});
	p[0] = board.~~createElement~~('point', [-1,-2], {style:4});		var f = board.lagrangePolynomial(p);
	p[1] = board.~~createElement~~('point', [6,5], {style:4});		var graph = board.create('functiongraph', [f,-10, 10]);
	p[2] = board.~~createElement~~('point', [-0.5,1], {style:4});
	p[3] = board.~~createElement~~('point', [3,3], {style:4});
	var f = board.lagrangePolynomial(p);
	var graph = board.~~createElement~~('functiongraph', [f, -10, 10]);

	var g = function(x) {		var g = function(x) {
	return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());		return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
	}		};

	var r = board.~~createElement~~('glider', [		var r = board.create('glider', [
	function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },		function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
	graph], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	board.~~createElement~~('tangent', [r], {strokeColor:'#ff0000'});		board.create('tangent', [r], {strokeColor:'#ff0000'});
	line = board.~~createElement~~('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});		line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});

	board.unsuspendUpdate();		board.unsuspendUpdate();

A WASSERMANN at 17:13, 29 October 2009

2009-10-29T17:13:45Z

← Older revision		Revision as of 17:13, 29 October 2009
Line 1:		Line 1:
	<html>		<html>
	<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />		<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>~~
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>		<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>

A WASSERMANN at 14:36, 10 March 2009

2009-03-10T14:36:20Z

← Older revision		Revision as of 14:36, 10 March 2009
Line 23:		Line 23:
	}		}

	var r = board.createElement('~~point~~', [		var r = board.createElement('glider', [
	function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); }		function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
	], {name:' ',style:6,fixed:true});		graph], {name:' ',style:6,fixed:true});
	~~var r2 = board.createElement('point', [function(){ return r.X()+0.01;},~~		board.createElement('tangent', [r], {strokeColor:'#ff0000'});
	~~function(){ return f(r.X()+0.01);}], {style:7,visible:false});~~

	~~line =~~ board.createElement('~~line~~',[r~~,r2~~],{strokeColor:'#ff0000'});
	line = board.createElement('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});		line = board.createElement('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});

Line 57:		Line 54:
	}		}

	var r = board.createElement('~~point~~', [		var r = board.createElement('glider', [
	function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },		function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); }],		function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
	{name:' ',style:6~~});~~		graph], {name:' ',style:6,fixed:true});
	~~var r2 = board.createElement('point', [~~		board.createElement('tangent', [r], {strokeColor:'#ff0000'});
	~~function(){ return r.X()+0.01;},~~
	~~function(){ return f(r.X()+0.01);}], {style:7~~,~~visible~~:~~false~~});


	~~line =~~ board.createElement('~~line~~',[r~~,r2~~],{strokeColor:'#ff0000'});
	line = board.createElement('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});		line = board.createElement('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});