use quarto, not Pluto to render pages

quarto/derivatives/optimization-trapezoid.js

@@ -0,0 +1,36 @@
+// inscribe trapezoid
+var R = 5;
+var Delta = 0.5
+const b = JXG.JSXGraph.initBoard('jsxgraph', {
+    boundingbox: [-R-Delta,R+Delta,R+Delta,-1], axis:true
+});
+
+var xax = b.create("segment", [[0,0],[R,0]]);
+
+var P4 = b.create("glider", [R/2,0, xax], {name: "P_4=(r,0)"});
+
+
+
+var CL = b.create('point', [function() {return -P4.X()},0], {name:''});
+var CR = b.create('point', [function() {return  P4.X()},0], {name:''});
+var C = b.create('semicircle', [CL,CR]);
+
+var Crestricted = b.create("functiongraph",
+			   [function(x) {
+			       r = P4.X();
+			       y = Math.sqrt(r*r - x*x);
+			       return y;
+			   }, 0, function() {return P4.X()}]);
+
+var P3 = b.create("glider", [
+    P4.X()/2,
+    Math.sqrt(P4.X()*P4.X()*(1 - 1/4)),
+    Crestricted], {name:"P_3=(x,y)"});
+
+var P1 = b.create('point', [function() {return -Math.abs(P4.X());},
+			    function() {return P4.Y();}], {name:'P_1'});
+var P2 = b.create('point', [function() {return -P3.X();},
+			    function() {return P3.Y();}], {name:'P_2'});
+
+var poly = b.create('polygon',[P1, P2, P3, P4], { borders:{strokeColor:'black'} });
+b.create('text',[-1.5,.25, function(){ return 'Area='+ poly.Area().toFixed(1); }]);