# Rolle's Theorem

### 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 = board.lagrangePolynomial(p);
var graph = board.createElement('functiongraph', [f, -10, 10]);

var r = board.createElement('glider', [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)); },graph],
{name:' ',style:6});
var t = board.createElement('tangent', [r], {strokeColor:'#ff0000'});
line = board.createElement('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});
board.unsuspendUpdate();