Newton's root finding method

x_o is the start value. Drag it.

You may change the function term here:

f(x) =

You also may try the following function terms:

• [math]\displaystyle{ Math.sin(x) }[/math]
• [math]\displaystyle{ Math.exp(x) }[/math]
• [math]\displaystyle{ Math.pow(2,x) }[/math]
• [math]\displaystyle{ 1-2/(x*x) }[/math]

The underlying JavaScript code

<table width="600" border="0" cellpadding="0" cellspacing="0">
x<sub>o</sub> is the start value. Drag it.
<p></p>
You may change the function term here:
<br>
<td><nobr>f(x) = </nobr></td>
<td>
<form>
<input style="border:none; background-color:#efefef;padding:5px;margin-left:2px;" type="text" id="graphterm" value="x*x*x/5" size="30"/><input type="button" value="set term" onClick="newGraph(document.getElementById('graphterm').value);">
</form>
</td>
<tr><td>&nbsp;</td></tr>
<script type="text/javascript">
// Initial function term
var term = function(x) { return x*x*x/5; };
var graph = function(x) { return term(x); };
	
// Recursion depth
var steps = 11;
// Start value
var s = 3;

for (i = 0; i < steps; i++) {
     document.write('<tr><td><nobr>x<sub>' + i + '</sub> = </nobr></td><td><font id="xv' + i + '"></font></td></tr>');
}
</script>		
</table> 
<jsxgraph width="600" height="500">

var i;
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,10,5,-2], axis:true});
var ax = board.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});
var ay = board.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});

var g = board.create('functiongraph', [function(x){return graph(x);}],{strokeWidth: 2, dash:0});
var x = board.create('glider',[s,0,ax], {name: 'x_{0}', strokeColor: 'magenta', fillColor: 'yellow'});

newGraph(document.getElementById('graphterm').value);
newton(x,steps);	
function xval(board) {
    for (i = 0; i < steps; i++)
        document.getElementById('xv' + i).innerHTML = board.round(JXG.getReference(board, 'x_{' + i + '}').X(),14);
}

board.addHook(xval);

function newton(p, i) {		
    if(i>0) {
        var f = board.create('glider',[function(){return p.X();}, function(){return graph(p.X())},g], {name: '', style: 3, strokeColor: 'green', fillColor: 'yellow'});
        var l = board.create('line', [p,f],{strokeWidth: 0.5, dash: 1, straightFirst: false, straightLast: false, strokeColor: 'black'});
        var t = board.create('tangent',[f],{strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
        var x = board.create('point',[board.intersection(ax,t,0)],{name: 'x_{'+(steps-i+1) + '}', style: 4, strokeColor: 'magenta', fillColor: 'yellow'});
        newton(x,--i);
    }
}	
function newGraph(v) {
	eval("term = function(x){ return "+v+";}");				
	graph = function(x) { return term(x); };
	g.Y = function(x){ return term(x); };
	g.updateCurve();
        board.update();
}

</jsxgraph>