GraphingCalculator 4;
Window 84 10 994 1161;
SignificantDigits 5;
FontSizes 18;
PaneDivider 776;
BackgroundType 0;
BackgroundColor 255 255 255;
StackPanes 1;
Slider 1 100;
SliderSteps 99;
SliderControlValue 0;
SliderOneDirection 1;
2D.Scale 0.25 0.5 1 2;
2D.BottomLeft -11.78125 -0.640625;
2D.GraphPaper 0;
Picture 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" 0.359375 7.46875;
Color 17;
Expr 'View'=slider([0,3,3]);
Text "n is the number of subintervals of [a, b].";
Color 17;
Expr function(f,x)=1-[x-2]^3;
Color 17;
Expr a=0,b=4;
Color 17;
Expr '∆x'=(b-a)/n;
Text "⬆︎∆x is the length of each subinterval";
Color 17;
Expr function(m,x,'∆x')=(function(f,x+'∆x')-function(f,x))/'∆x';
Text "⬆︎m(x,∆x) is the average rate of change (as clarified earlier) of the function f over the interval [x, x+∆x].";
Color 17;
Expr function(r,x,q)=function(m,q*'∆x','∆x')*[x-(q*'∆x')]+function(f,q*'∆x');
Text "⬆︎r(x,q) is the function having a constant rate of change equal to the average rate of change of f over the qth subinterval and agreeing with f at the beginning and end of the qth subinterval
";
Color 8;
Expr y=function(f,x),akth subinterval contained in [a,b] for all k from 0 to 100.";
Expr vector(x,y)=[if(vector(a+k*'∆x',function(m,a+k*'∆x','∆x')),And(['View'=2,a+k*'∆x'kth subinterval contained in [a,b] for all k from 0 to 100.";
Color 3;
Expr y=[if(function(m,k*'∆x','∆x'),And(['View'=3,notequal(x,k*'∆x'),k*'∆x'f and r over kth subinterval for all k from 0 to 100.";