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 = [];
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
p[0] = board.create('point', [-1,2], {size:3,face:'x',fixed:true});
        b1axisy = 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 polynomial = function(x) {
board.unsuspendUpdate();
                var i;
</jsxgraph>
                var y = 0.0;
 
                var xc = [];
=== The underlying JavaScript code ===
                for (i=0;i<p.length;i++) {
<source lang="javascript">
                  xc[i] = p[i].X();
board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});
                }
board.suspendUpdate();
                for (i=0;i<p.length;i++) {
var p = [];
                  var t = p[i].Y();
p[0] = board.create('point', [-1,2], {size:3,face:'x',fixed:true});
                  for (var k=0;k<p.length;k++) {
p[1] = board.create('point', [6,2], {size:3,face:'x',fixed:true});
                    if (k!=i) {
p[2] = board.create('point', [-0.5,1], {size:2});
                      t *= (x-xc[k])/(xc[i]-xc[k]);
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]);
                  y += t;
                }
                return y;
            };
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});


q = board.createElement('glider', [4.5,0,graph], {style:6});
var r = board.create('glider', [function() { return JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5); },
q2 = board.createElement('point', [function(){ return q.X()+0.01;},
                                function() { return f(JXG.Math.Numerics.root(JXG.Math.Numerics.D(f),(p[0].X()+p[1].X())*0.5)); },graph],  
      function(){ return polynomial(q.X()+0.01);}], {style:7,visible:false});
                                {name:' ',size:4});
line = board.createElement('line',[q,q2],{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();
</script>
</source>
</html>
 


[[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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