Rolle's Theorem: Difference between revisions

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<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/prototype.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>
<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 = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f, -10, 10]);


        var p = [];
var r = board.create('glider', [function() { return JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5); },
        p[0] = board.createElement('point', [-1,2], {style:1,fixed:true});
                                function() { return f(JXG.Math.Numerics.root(JXG.Math.Numerics.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 = JXG.Math.Numerics.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 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:' ',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]]

Latest revision as of 15:52, 20 February 2013

The underlying JavaScript code

board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});
board.suspendUpdate();
var p = [];
p[0] = board.create('point', [-1,2], {size:3,face:'x',fixed:true});
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 = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f, -10, 10]);

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