(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.
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.