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('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();