The average rate of change of a function on the interval [a,b] is the slope of the secant line through (b(,f(b) and (a,f(a)), and is dependent upon the values of a and b specified.
The instantaneous rate of change of that function on the same interval is the LIMIT of this average rate of change of the function as h becomes smaller and smaller. This limit is called the "derivative" of the function f(x).
