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 20:40, 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();