Calculate the average rate of change of the function $f(x) = x^3 - 3x^2$ between the given values.
a. Find the average rate of change on the interval $[-3, -2]$.
b. Find the average rate of change on the interval $[-2, -1.9]$.
c. Find the average rate of change on the interval $[-2, -1.99]$.
d. Find the average rate of change on the interval $[-2, -1.999]$.
e. Based on your previous answers, estimate the instantaneous rate of change at $x = -2$.