Let be a function that is differentiable on [a, b]. We defined the average rate of change of over [a, b] to be

Let ƒ be a function that is differentiable on [a, b]. We defined the average rate of change of ƒ over [a, b] to be

and the instantaneous rate of change of ƒ at x to be ƒ′(x). In this chapter we defined the average value of a function. For the new definition of average to be consistent with the old one, we should have

Is this the case? Give reasons for your answer.

f(b) = f(a) b - a