Explain the difference between the average rate of change of y as x changes from a to b, and the instantaneous rate of change of y at x

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).