<< Graphics`Arrow`

f[x_] = (((x - (3/4)))^3) -  .7 (x - (3/4))  ;
a = 0.55;
m[a_, h_] := ((f[a + h] - f[a])/h);
TANGENT[x_] := 
        m[a, h] (x - a) + f[a];
DQ = {};

For[h = 1.5, h > 0, h = h - 0.01, 
        DQ = {DQ, 
            PLOT = Plot[{f[x], TANGENT[x]}, {x, a -  .4, a + 1.75}, 
                Axes -> False, 
                DisplayFunction -> 
                  Identity]; 
Show[{PLOT, 
                Graphics[{Arrow[{a, f[a] - 1}, {a + h, f[a] - 1}], 
                    Arrow[{a + h, f[a] - 1}, {a, f[a] - 1}], 
                    Text["h", {a + (h/2), f[a] - 1}, {0, 2}], 
                    Arrow[{a - 0.3, f[a]}, {a - 0.3, f[a + h]}], 
                    Arrow[{a - 0.3, f[a + h]}, {a - 0.3, f[a]}], 
                    Text["f[a+h]-f[a]", {a - 
                          0.3, ((f[a + h] + f[a])/2)}, {1, 0}]}]}, 
              PlotRange -> All, 
              DisplayFunction -> $DisplayFunction]}];
DQ = Flatten[DQ];

SetDirectory["D:\My Documents\My \
Webs\myweb\Spring_2002\Math_124_Spring_2002_Noon\Graphics"]; 
    Export["difference_quotient.gif", 
      DQ, "GIF", "Transparency" -> 
        GrayLevel[1], "Loop" -> True, 
      ImageResolution -> 72];

(lim_(h -> 0))((f(a + h) - f(a))/h)