Mean Value Theorem

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
board.suspendUpdate();
var p = [];
p[0] = board.create('point', [-1,-2], {style:4});
p[1] = board.create('point', [6,5], {style:4});
p[2] = board.create('point', [-0.5,1], {style:4});
p[3] = board.create('point', [3,3], {style:4});
var f = board.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10]);

var g = function(x) {
     return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
};

var r = board.create('glider', [
                    function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
                    function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
                    graph], {name:' ',style:6,fixed:true});
board.create('tangent', [r], {strokeColor:'#ff0000'});
line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});

board.unsuspendUpdate();