2.4 Average Rate of Change of a Function
Ideas in this lesson
- Distinguish net change, average rate, and units
- Calculate rates from polynomial formulas
- Simplify rational and radical difference quotients
- Derive symbolic difference quotients
- Read graphs and secant slopes
- Compare rates in tables and changing data
- Relate signs and successive rates to behavior
- Use constant rates and justify linear behavior
- Interpret motion, laps, and race graphs
- Investigate shrinking intervals without assuming calculus
Distinguish net change, average rate, and units · Worked example
A measured ticket sales changes from 42 to 62 tickets during 4 days. Give the net change and average rate, including units.
Answer: 20 tickets; 5 tickets per day
Net change is final minus initial: 62−42=20 tickets.
Divide by elapsed input 4: 20/4=5.
The output/input units are tickets per day; the quotient is a secant rate.
Divide by elapsed input 4: 20/4=5.
The output/input units are tickets per day; the quotient is a secant rate.