1. Warm-Up: 𝑓(−3) 𝑓 2 𝑓(1) 𝑓(𝑓 3 )
Given the graph of 𝑓(𝑥), find the following indicated values.
𝑓(−3)
𝑓 2
𝑓(1)
𝑓(𝑓 3 )

3. 50 75
125
200

4. Average Rate of Change
The average rate of change of 𝑓(𝑥) with respect to x, as x changes from a to b is:

5. Example 1:
A large heavy-duty balloon is being filled with water. Its approximate volume (in gallons) is given by: 𝑉 𝑥 = 𝑥 where x is the radius of the balloon (in inches). Find the average rate of change of the volume of the balloon as the radius increases from 5 to 10 inches.

6. Example 2:
According to the Encyclopedia Britannica almanac, these are the estimated number of cell phone users in the United States, from 1993 to Let 𝑓(𝑡) be the number of cell phone users in year 𝑡. Find the average rate of change in cell phone use during the following time periods: a) b)

7. Closure:
Which represents the average rate of change formula?

9. #3)
We can conclude that the average rate of change is the slope of a secant line!

10. Example 1:
Find the equation of the secant line to the curve 𝑓 𝑥 =4 𝑥 2 −7 on the interval [-2,1].

11. Example 2:
Find the equation of the secant line to the curve 𝑓 𝑥 = 𝑥 4 +5 𝑥 3 −𝑥−5 on the interval [-5,3].

12. Example 3:
Find the equation of the secant line to the curve 𝑓 𝑥 = 𝑥 2 +2𝑥 on the interval [3,5].