(a) Define the term “average rate of change” of a real-valued function on a closed interval and describe geometrically what it represents.
(a) Define the term “average rate of change” of a real-valued function on a closed interval and describe geometrically what it represents.
(b) Distinguish between the average rate of change of a function on an interval and the instantaneous rate of change at a point.
(c) Explain what happens to the average rate of change as the second point on the curve approaches the first point, and state the limiting quantity obtained.