# Lagrange interpolation

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Constructs a polynomial of degree $n$ through $n+1$ given points. Points can be added by clicking on "Add point". The dotted line is the graph of the first derivative, the dashed line is the graph of the second derivative.

### 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});

function addPoint() {
p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
board.update();
}