(*^

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                       Derivatives -- Comparing a Function and Its Derivative

The following cell reminds you of the syntax for the Mathematica   Plot  procedure that you will want to use to draw graphs for this module.  Evaluate the next cell now.  The specification AspectRatio -> Automatic  causes Mathematica  to draw the graph so that one physical unit on the x-axis represents the same change in x as one physical unit on the y-axis represents for y.  This specification is optional but is nice to include in these graphs because we are interested in the relationship between a function and its derivative.  When different scales are used for the two axes the slope of a curve is somehwat distorted.  To see this effect evaluate the cell following the next cell.
;[s]
14:0,3;77,0;132,2;143,0;146,3;150,0;221,1;250,0;268,4;292,0;301,2;313,0;707,1;768,0;769,-1;
5:7,13,9,Times,0,12,0,0,0;2,13,9,Times,1,12,65535,0,0;2,13,9,Times,2,12,0,0,0;2,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,65535;
:[font = input; preserveAspect; ]
Fcn[x_] := Sin[x]
low := -Pi
high := Pi
h := 0.001

Deriv[x_] := (Fcn[x + h] - Fcn[x])/h

Plot[{Fcn[x], Deriv[x]}, {x, low, high},
      AspectRatio -> Automatic]
;[s]
3:0,0;137,1;161,0;163,-1;
2:2,12,10,Courier,1,12,0,0,0;1,12,10,Courier,1,12,65535,0,65535;
:[font = input; preserveAspect; ]
Plot[{Fcn[x], Deriv[x]}, {x, low, high}]
^*)