# Difference between revisions of "Rolle's Theorem"

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### The underlying JavaScript code

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

var p = [];
p[0] = board.createElement('point', [-1,2], {style:1,fixed:true});
p[1] = board.createElement('point', [6,2], {style:1,fixed:true});
p[2] = board.createElement('point', [-0.5,1], {style:4});
p[3] = board.createElement('point', [2,0.5], {style:4});
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;
};
var graph = board.createElement('curve', ['x', f, 'x', -10, 10], {curveType:'graph'});

var r = board.createElement('point', [function() { return board.root(board.D(f),(p[0].X()+p[1].X())*0.5); },
function() { return f(board.root(board.D(f),(p[0].X()+p[1].X())*0.5)); }],
{name:' ',style:6});
var r2 = board.createElement('point', [function(){ return r.X()+0.01;},
function(){ return f(r.X()+0.01);}], {style:7,visible:false});

line = board.createElement('line',[r,r2],{strokeColor:'#ff0000'});
line = board.createElement('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});

board.unsuspendUpdate();