Rolle's Theorem - Revision history

A WASSERMANN at 15:52, 20 February 2013

2013-02-20T15:52:38Z

← Older revision		Revision as of 15:52, 20 February 2013
Line 10:		Line 10:
	var graph = board.create('functiongraph', [f, -10, 10]);		var graph = board.create('functiongraph', [f, -10, 10]);

	var r = board.create('glider', [function() { return ~~board~~.root(~~board~~.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.create('glider', [function() { return JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(~~board~~.root(~~board~~.D(f),(p[0].X()+p[1].X())*0.5)); },graph],		function() { return f(JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',size:4});		{name:' ',size:4});
	var t = board.create('tangent', [r], {strokeColor:'#ff0000'});		var t = board.create('tangent', [r], {strokeColor:'#ff0000'});
Line 30:		Line 30:
	var graph = board.create('functiongraph', [f, -10, 10]);		var graph = board.create('functiongraph', [f, -10, 10]);

	var r = board.create('glider', [function() { return ~~board~~.root(~~board~~.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.create('glider', [function() { return JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(~~board~~.root(~~board~~.D(f),(p[0].X()+p[1].X())*0.5)); },graph],		function() { return f(JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',size:4});		{name:' ',size:4});
	var t = board.create('tangent', [r], {strokeColor:'#ff0000'});		var t = board.create('tangent', [r], {strokeColor:'#ff0000'});

A WASSERMANN at 15:51, 20 February 2013

2013-02-20T15:51:57Z

← Older revision		Revision as of 15:51, 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', [2,0.5], {size:2});		p[3] = board.create('point', [2,0.5], {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 27:		Line 27:
	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', [2,0.5], {size:2});		p[3] = board.create('point', [2,0.5], {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 12:37, 8 June 2011

2011-06-08T12:37:45Z

← Older revision		Revision as of 12:37, 8 June 2011
Line 1:		Line 1:
	<~~html>~~		<jsxgraph box="box" width="600" height="400">
	~~<link rel="stylesheet" type="text/css" href="http://~~jsxgraph~~.uni-bayreuth.de/distrib/jsxgraph.css" />~~		board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});
	~~<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~~">
	board = JXG.JSXGraph.initBoard('box', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 50~~, ~~unitY~~: 25});
	board.suspendUpdate();		board.suspendUpdate();
	~~// Axes~~		var p = [];
	~~xax~~ = board.~~createElement~~('~~axis~~', [[0,0], [1,0]], {});		p[0] = board.create('point', [-1,2], {size:3,face:'x',fixed:true});
	~~yax~~ = board.~~createElement~~('~~axis~~', [[0,0], [0~~,1]~~], {});		p[1] = board.create('point', [6,2], {size:3,face:'x',fixed:true});
			p[2] = board.create('point', [-0.5,1], {size:2});
			p[3] = board.create('point', [2,0.5], {size:2});
			var f = board.lagrangePolynomial(p);
			var graph = board.create('functiongraph', [f, -10, 10]);

	~~var p = [];~~		var r = board.create('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	~~p[0] = board.createElement('point', [-1,2], {style:1,fixed:true});~~		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	~~p[1] = board.createElement('point', [6,2], {style:1,fixed:true});~~		{name:' ',size:4});
	~~p[2] = board.createElement('point', [-0.5,1], {style:4});~~		var t = board.create('tangent', [r], {strokeColor:'#ff0000'});
	~~p[3] = board.createElement('point', [2,0.5], {style:4});~~		line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});
	~~var f = board.lagrangePolynomial(p);~~
	~~var graph = board.createElement('functiongraph', [f, -10, 10]);~~

	var r = board.~~createElement~~('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',~~style~~:6});
	var t = board.~~createElement~~('tangent', [r], {strokeColor:'#ff0000'});
	line = board.~~createElement~~('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});
	board.unsuspendUpdate();		board.unsuspendUpdate();
	</~~script>~~		</jsxgraph>
	~~</html~~>

	=== 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});		board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});
	board.suspendUpdate();		board.suspendUpdate();
	~~// Axes~~		var p = [];
	~~xax = board.createElement('axis', [[0,0], [1,0]], {});~~		p[0] = board.create('point', [-1,2], {size:3,face:'x',fixed:true});
	~~yax = board.createElement('axis', [[0,0], [0,1]], {});~~		p[1] = board.create('point', [6,2], {size:3,face:'x',fixed:true});
			p[2] = board.create('point', [-0.5,1], {size:2});
	var p = [];		p[3] = board.create('point', [2,0.5], {size:2});
	p[0] = board.~~createElement~~('point', [-1,2], {~~style~~:1,fixed:true});		var f = board.lagrangePolynomial(p);
	p[1] = board.~~createElement~~('point', [6,2], {~~style~~:1,fixed:true});		var graph = board.create('functiongraph', [f, -10, 10]);
	p[2] = board.~~createElement~~('point', [-0.5,1], {~~style~~:4});
	p[3] = board.~~createElement~~('point', [2,0.5], {~~style~~:4});
	var f = board.lagrangePolynomial(p);
	var graph = board.~~createElement~~('functiongraph', [f, -10, 10]);

	var r = board.~~createElement~~('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.create('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',~~style~~:6});		{name:' ',size:4});
	var t = board.~~createElement~~('tangent', [r], {strokeColor:'#ff0000'});		var t = 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();
	</source>		</source>


	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Calculus]]		[[Category:Calculus]]

A WASSERMANN at 17:26, 29 October 2009

2009-10-29T17:26:49Z

← Older revision		Revision as of 17:26, 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 14:34, 10 March 2009

2009-03-10T14:34:56Z

← Older revision		Revision as of 14:34, 10 March 2009
Line 19:		Line 19:
	var graph = board.createElement('functiongraph', [f, -10, 10]);		var graph = board.createElement('functiongraph', [f, -10, 10]);

	var r = board.createElement('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.createElement('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',style:6});		{name:' ',style:6});
	var r2 = board.createElement('tangent', [r~~]); //function(){ return r.X()+0.01;},~~		var t = 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});

	board.unsuspendUpdate();		board.unsuspendUpdate();
	</script>		</script>
Line 49:		Line 44:
	var graph = board.createElement('functiongraph', [f, -10, 10]);		var graph = board.createElement('functiongraph', [f, -10, 10]);

	var r = board.createElement('~~point~~', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.createElement('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); }],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',style:6});		{name:' ',style:6});
	var r2 = board.createElement('~~point', [function(){ return r.X()+0.01;},~~		var t = 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});

	board.unsuspendUpdate();		board.unsuspendUpdate();
	</source>		</source>
	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Calculus]]		[[Category:Calculus]]

A WASSERMANN at 14:33, 10 March 2009

2009-03-10T14:33:58Z

← Older revision		Revision as of 14:33, 10 March 2009
Line 26:		Line 26:


	line = board.createElement('line',[r,r2],{strokeColor:'#ff0000'});		//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});

A WASSERMANN at 14:33, 10 March 2009

2009-03-10T14:33:23Z

← Older revision		Revision as of 14:33, 10 March 2009
Line 22:		Line 22:
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',style:6});		{name:' ',style:6});
	var r2 = board.createElement('~~point~~', [function(){ return r.X()+0.01;},		var r2 = board.createElement('tangent', [r]); //function(){ return r.X()+0.01;},
	function(){ return f(r.X()+0.01);}], {style:7,visible:false});		// function(){ return f(r.X()+0.01);}], {style:7,visible:false});

A WASSERMANN at 14:32, 10 March 2009

2009-03-10T14:32:45Z

← Older revision		Revision as of 14:32, 10 March 2009
Line 19:		Line 19:
	var graph = board.createElement('functiongraph', [f, -10, 10]);		var graph = board.createElement('functiongraph', [f, -10, 10]);

	var r = board.createElement('~~point~~', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.createElement('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); }],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',style:6});		{name:' ',style:6});
	var r2 = board.createElement('point', [function(){ return r.X()+0.01;},		var r2 = board.createElement('point', [function(){ return r.X()+0.01;},

A WASSERMANN at 12:10, 10 March 2009

2009-03-10T12:10:26Z

← Older revision		Revision as of 12:10, 10 March 2009
Line 19:		Line 19:
	var graph = board.createElement('functiongraph', [f, -10, 10]);		var graph = board.createElement('functiongraph', [f, -10, 10]);

	var r = board.createElement('~~glider~~', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.createElement('point', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); }~~,graph~~],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); }],
	{name:' ',style:6});		{name:' ',style:6});
	var r2 = board.createElement('point', [function(){ return r.X()+0.01;},		var r2 = board.createElement('point', [function(){ return r.X()+0.01;},

A WASSERMANN at 12:10, 10 March 2009

2009-03-10T12:10:00Z

← Older revision		Revision as of 12:10, 10 March 2009
Line 19:		Line 19:
	var graph = board.createElement('functiongraph', [f, -10, 10]);		var graph = board.createElement('functiongraph', [f, -10, 10]);

	var r = board.createElement('~~point~~', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },		var r = board.createElement('glider', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
	function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); }],		function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); },graph],
	{name:' ',style:6});		{name:' ',style:6});
	var r2 = board.createElement('point', [function(){ return r.X()+0.01;},		var r2 = board.createElement('point', [function(){ return r.X()+0.01;},