# Newton's root finding method

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xo is the start value. Drag it.

You may change the function term here, Try also the following function terms:
• sin(x)
• exp(x)
• 2^x
• 1-2/(x*x)

 f(x) =

### 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">
// Get initial function term
var term = document.getElementById('graphterm').value;

// Recursion depth
var steps = 11;

// Start value for x
var x_0 = 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>

var i;
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});
var ax = brd.defaultAxes.x;

var g = brd.create('functiongraph', [term], {strokeWidth: 2});
var x = brd.create('glider', [x_0, 0, ax], {name: 'x_{0}', color: 'magenta', size: 4});

newGraph(document.getElementById('graphterm').value);
newton(x, steps, brd);

function xval() {
for (i = 0; i < steps; i++) {
document.getElementById('xv' + i).innerHTML = (brd.select('x_{' + i + '}').X()).toFixed(14);
}
}

brd.on('update', xval);
// Initial call of xval()
xval();

function newton(p, i, board) {
board.suspendUpdate();
if (i > 0) {
var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {
name: '', style: 3, color: 'green'});
var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});
var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});
newton(x, --i, board);
}
board.unsuspendUpdate();
}

function newGraph(v) {
g.generateTerm('x', 'x', v);
//g.updateCurve();
brd.update();
}