Mathematica Tool 3

This Mathematica file is written to accompany Section 2.4. It is configured to graph the approximate derivative of f(t)=(e^(k t)) and to determine how the derivative is related to f  itself.

Enter the value of k (initially set to 1).

k=1;
f[t_]:=(E^(k t))
g[t_]:=((f[t+0.001]-f[t])/0.001)
h[t_]:=((g[t])/(f[t]))

Plot the functions f, g, and h.

Plot[{f[t],g[t],h[t]},{t,-2,2},PlotRange->{{-2,2},{0,8}},PlotStyle->{{Red, Thickness[0.01]},{Blue,Thickness[0.01]},{Green,Thickness[0.01]}}]