update work flow

This commit is contained in:
jverzani
2022-07-25 20:51:08 -04:00
parent bce4ce7fa0
commit 6712bb02c4
86 changed files with 489 additions and 2139 deletions

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@@ -396,7 +396,39 @@ That is the function $f(x)$, minus the secant line between $(a,f(a))$ and $(b, f
nothing
```
An interactive example can be found at [jsxgraph](http://jsxgraph.uni-bayreuth.de/wiki/index.php?title=Mean_Value_Theorem).
```=html
<div id="jsxgraph" style="width: 500px; height: 500px;"></div>
```
```ojs
//| echo: false
//| output: false
JXG = require("jsxgraph");
board = JXG.JSXGraph.initBoard('jsxgraph', {boundingbox: [-5, 10, 7, -6], axis:true});
p = [
board.create('point', [-1,-2], {size:2}),
board.create('point', [6,5], {size:2}),
board.create('point', [-0.5,1], {size:2}),
board.create('point', [3,3], {size:2})
];
f = JXG.Math.Numerics.lagrangePolynomial(p);
graph = board.create('functiongraph', [f,-10, 10]);
g = function(x) {
return JXG.Math.Numerics.D(f)(x)-(p[1].Y()-p[0].Y())/(p[1].X()-p[0].X());
};
r = board.create('glider', [
function() { return JXG.Math.Numerics.root(g,(p[0].X()+p[1].X())*0.5); },
function() { return f(JXG.Math.Numerics.root(g,(p[0].X()+p[1].X())*0.5)); },
graph], {name:' ',size:4,fixed:true});
board.create('tangent', [r], {strokeColor:'#ff0000'});
line = board.create('line',[p[0],p[1]],{strokeColor:'#ff0000',dash:1});
```
This interactive example can also be found at [jsxgraph](http://jsxgraph.uni-bayreuth.de/wiki/index.php?title=Mean_Value_Theorem). It shows a cubic polynomial fit to the ``4`` adjustable points labeled A through D. The secant line is drawn between points A and B with a dashed line. A tangent line -- with the same slope as the secant line -- is identified at a point ``(\alpha, f(\alpha))`` where ``\alpha`` is between the points A and B. That this can always be done is a conseuqence of the mean value theorem.
##### Example