GraphingCalculator 4;
Window 47 3 861 1262;
PaneDivider 477;
SignificantDigits 14;
FontSizes 18;
StackPanes 1;
2D.Scale 0.1 0.1 5 5;
2D.BottomLeft -2.2 -0.35625;
2D.GraphPaper 0;
Text "Illustration of the derivative as limiting slope of tangent line.
Conditionals currently assume f>0 on region of interest, and some other details of shape of chosen f.

Function and its inverses.  (+/-1 give smaller and larger.)";
Expr function(f,x)=1/([x-2]^4+c^4)+0.1;
Color 6;
Expr function(F_L,x)=[-1]*[1/(x-0.1)-c^4]^(1/4)+2;
Color 2;
Expr function(F_R,x)=[1/(x-0.1)-c^4]^(1/4)+2;
Color 5;
MathPaneSlider 38;
Expr c=slider([0,1,40]);
Color 8;
Expr function(f,x);
Text "Left and right points; d = width of interval.   (Take b>a i.e. d>0 for now.)
";
Color 3;
MathPaneSlider 60;
Expr a=slider([-1,4]);
Color 4;
Expr d=slider([0.001,4,100]);
Color 7;
Expr b=a+d;
Color 8;
Expr vector(x,y)=vector(a,function(f,a));
Color 8;
Expr vector(x,y)=vector(b,function(f,b));
Color 6;
Expr function(M,x)=function(oppartial(x),function(f,x));
Color 7;
Expr function(m,a,b)=(function(f,b)-function(f,a))/(b-a);
Text "Tangent line at a and line connecting (a,f(a)) to (b,f(b)):";
Color 17;
Expr y-function(f,a)=function(M,a)*[x-a];
Color 17;
Expr y-function(f,b)=function(m,a,b)*[x-b];
Color 17;
Expr y-function(f,b)=function(m,a,b)*[x-b],a<x<b;
Text "Triangle enclosed by line:";
Color 17;
Expr a<x<b,function(f,a)<y<function(m,a,b)*[x-a]+function(f,a);
Color 17;
Expr a<x<b,function(f,b)<y<function(m,a,b)*[x-a]+function(f,a);
Text "Run and rise marked on axes:";
Color 17;
Expr a<x<b,-0.01<y<0.01;
Color 17;
Expr -0.01<x<0.01,function(f,a)<y<function(f,b);
Color 17;
Expr -0.01<x<0.01,function(f,b)<y<function(f,a);
Text "Run and rise marked as regions:";
Color 17;
Expr a<x<b,0<y<function(f,x);
Color 17;
Expr function(f,a)<y<function(f,b),0<x<function(F_L,y);
Color 17;
Expr function(f,b)<y<function(f,a),0<x<function(F_R,y);
Text "Rate of change	";
Color 17;
Expr function(oppartial(x),function(f,x));
Color 17;
Expr function(oppartial(x),function(oppartial(x),function(f,x)));
Color 17;
Expr 1/2*function(oppartial(x),function(oppartial(x),function(f,x)));
Text "

<size=16>Author: David A. Craig  <<http://web.lemoyne.edu/~craigda/>";
PageMargins 72 72 72 72;