# Lagrange interpolation

Constructs a polynomial of degree $n$ through $n+1$ given points. Points can be added by clicking on "Add point".

### The underlying JavaScript code

<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>
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>

        board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
// Axes
b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
b1axisy = board.createElement('axis', [[0,0], [0,1]], {});

var p = [];
p[0] = board.createElement('point', [-1,2], {style:6});
p[1] = board.createElement('point', [3,-1], {style:6});

var f = function(x) {
var i;
var y = 0.0;
var xc = [];
for (i=0;i<p.length;i++) {
xc[i] = p[i].X();
}
for (i=0;i<p.length;i++) {
var t = p[i].Y();
for (var k=0;k<p.length;k++) {
if (k!=i) {
t *= (x-xc[k])/(xc[i]-xc[k]);
}
}
y += t;
}
return y;
};
graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph'});
d1 = board.createElement('curve', ['x', board.D(f), 'x', -10, 10], {curveType:'graph',dash:1});
d2 = board.createElement('curve', ['x', board.D(board.D(f)), 'x', -10, 10], {curveType:'graph',dash:2});