Difference between revisions of "Mean Value Theorem"

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Line 54: Line 54:
 
</script>
 
</script>
 
</html>
 
</html>
 +
 +
<source lang="javascript">
 +
        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:4});
 +
        p[1] = board.createElement('point', [6,5], {style:4});
 +
        p[2] = board.createElement('point', [-0.5,1], {style:4});
 +
        p[3] = board.createElement('point', [3,3], {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 g = function(x) {
 +
        return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
 +
        }
 +
 +
    var r = board.createElement('point', [
 +
                    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)); }],
 +
        {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();
 +
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Revision as of 19:40, 21 January 2009

        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:4});
        p[1] = board.createElement('point', [6,5], {style:4});
        p[2] = board.createElement('point', [-0.5,1], {style:4});
        p[3] = board.createElement('point', [3,3], {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 g = function(x) {
         return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
        }

    var r = board.createElement('point', [
                    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)); }], 
         {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();