AP Calculus AB
Average Rate of Change Review Notes
AVERAGE RATE OF CHANGE AND SLOPES OF LINES: The average rate of change of
a function f  x  over an interval between two points  a, f  a   and  b, f  b   is the slope of
the secant line connecting the two points:

For example, to calculate the average rate of change between the points:
 0, 2    0, f  0  
and  3, 28    3, f  3 
where f  x   3x 2  x  2 we would calculate:
What is the average rate of change between  1, f  1  and  2, f  2   for the same function?
Average Rate of Change as a function with respect to time. (Time is the independent
variable.)
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑟𝑎𝑣𝑒𝑙 𝑡𝑖𝑚𝑒
=
From the AP Exam 2010
Velocity Function:
We can calculate the average rate of change with respect to time for any quantity that changes
over time. On Friday the block one class will investigate the average rate of change in the
number of students as they exit the school building and proceed to the stadium during the
Emergency Response Plan drill. (The block two and four classes will have other opportunities to
gather similar types of data later.) The class will be divided into small groups stationed at the
school exits and, using “clicker counter” apps on their phones, will count the number of students
exiting the school over specific time intervals. We will use this data to help understand the
fundamentals of Calculus and its application to real world scenarios.