Mathematica Tool 1

This Mathematica file is written to accompany Section 2.4. It is configured to graph an exponential function,its derivative and their ratio.

Enter the base for the exponential function (b^t)

b=2;
f[t_]:=(b^t)

Define a function g(t) that approximates the derivative of f.

g[t_]:=((f[t+0.001]-f[t])/0.001)

Plot the functions f and g and thier ration (g/f)

Plot[{f[t],g[t],((g[t])/(f[t]))},{t,-2,2},PlotStyle->{{Red, Thickness[0.01]},{Blue,Thickness[0.01]},{Green,Thickness[0.01]}},PlotRange->{{-2,2},{0,4}},AxesLabel->{t,None}]