For a function f that is differentiable at x=a, which one of the following statements correctly describes the relationship between the average rate of change on [a,a+h] and the derivative f′(a) as h→0?
a) The average rate of change equals f′(a) for every non-zero h.
b) The average rate of change approaches 0 as h→0.
c) The average rate of change approaches f′(a) as h→0.
d) The average rate of change becomes unbounded as h→0.