Cauchy's mean value theorem: Difference between revisions

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''Cauchy's mean value theorem'' is also known as ''extended mean value theorem''. In Germany it is called ''Zweiter Mittelwertsatz''.
''Cauchy's mean value theorem'' is also known as ''extended mean value theorem''. In Germany it is called ''Zweiter Mittelwertsatz''.
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<jsxgraph width="600" height="400">
<jsxgraph width="600" height="400">
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,8,7,-8], axis:true});
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,8,7,-8], axis:true});
board.suspendUpdate();
board.suspendUpdate();
var p = [];
var p = [];
p[0] = board.create('point', [-1,-2], {style:4});
p[0] = board.create('point', [0,1], {style:4});
p[1] = board.create('point', [1,4], {style:4});
p[1] = board.create('point', [1,2], {style:4});
p[2] = board.create('point', [-0.5,1], {style:4});
p[2] = board.create('point', [2.5,3], {style:4});
p[3] = board.create('point', [3,3], {style:4});
p[3] = board.create('point', [3,2], {style:4});
p[4] = board.create('point', [-2,5], {style:4});
p[4] = board.create('point', [4,1], {style:4});
var graph = board.create('curve', board.neville(p),{strokeWidth:3,strokeOpacity:0.5});
var fArray = JXG.Math.Numerics.Neville(p);
var graph = board.create('curve', fArray, {strokeWidth:3,strokeOpacity:0.5});
/*
/*
var g = function(x) {
 
     return board.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
var g = function(t) {
     return JXG.Math.Numerics.D(fArray[0])(t)/JXG.Math.Numerics.D(fArray[1])(t)-(p[4].X()-p[0].X())/(p[4].Y()-p[0].Y());
};
};


var r = board.create('glider', [
var r = board.create('glider', [
                     function() { return board.root(g,(p[0].X()+p[1].X())*0.5); },
                     function() { return fArray[0](board.root(g,2)); },
                     function() { return f(board.root(g,(p[0].X()+p[1].X())*0.5)); },
                     function() { return fArray[1](board.root(g,2)); },
                     graph], {name:' ',style:6,fixed:true});
                     graph], {name:' ',style:6,fixed:true});
board.create('tangent', [r], {strokeColor:'#ff0000'});
board.create('tangent', [r], {strokeColor:'#ff0000'});

Latest revision as of 19:06, 18 January 2013

Cauchy's mean value theorem is also known as extended mean value theorem. In Germany it is called Zweiter Mittelwertsatz.

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