GraphingCalculator 4;
Window 45 0 865 1355;
PaneDivider 355;
SignificantDigits 3;
FontSizes 18;
BackgroundType 0;
StackPanes 1;
U -0.5 0.5;
V -0.5 0.5;
3D.View -0.5717970503756279 0.7062112071481199 0.4175091188507191 -0.5546332885907965 -0.7077559616136073 0.4375653256723404 0.6045081046703116 0.0186341069590012 0.7963810153997305;
3D.Speed 0;
Text "Gradient as normal vector.";
Color 7;
Expr function(f,x,y)=s*cos(x)*cos(y);
Color 5;
MathPaneSlider 51;
Expr a=slider([-2,2]);
Color 6;
MathPaneSlider 109;
Expr b=slider([-2,2]);
Color 3;
MathPaneSlider 109;
Expr s=slider([1,10]);
Text "Adjusting the sliders moves the normal vector.";
Color 4;
Expr function(g,x,y)=function(oppartial(x),function(f,x,y)),function(h,x,y)=function(oppartial(y),function(f,x,y));
Color 6;
Expr z=function(f,x,y);
Text "The trick here is we are plotting the normal to surfaces of constant g(x,y,z)=z-f(x,y) (=0, as plotted.)  Thus we plot grad g.";
MathPaneSlider 88;
Expr m=slider([0,0.1]);
Color 2;
Expr vector(a,b,function(f,a,b)),vector(a,b,function(f,a,b))+vector(-function(g,a,b),-function(h,a,b),1),'radius'=m;