Cogito
AP Precalculus · Chapter 1 · Lesson 1
Average Rate of Change
The slope between two points on any curve.
11 problems · about 22 minutes · AP Precalculus 1.1, 1.2
Figure — use these to answer the problems
- Point(-2, 0)
- Second point(3, 5)
- Slope between them1
Warm Up
Straightforward practice. Get the method working first.
4 problemsf(x) = x². Average rate of change on [3, 6]?
Answerf(x) = x². Average rate of change on [2, 5]?
Answerf(x) = 3x + 1. Average rate of change on [0, 10]?
Answerf(x) = x². Average rate of change on [−3, 3]?
Answer
Build It Up
The same ideas with more to keep track of.
3 problemsf(x) = x³. Average rate of change on [0, 2]?
AnswerSelect every statement that must be true when the average rate of change on [a, b] is 0.
- f(a) and f(b) are equal.
- The function need not be constant in between.
- The function is constant on the whole interval.
- f(a) and f(b) are both zero.
- Tick every box that applies.
Put these steps in the order you would carry them out.
Write 1 to 4 in the boxes to put these in order.
- Work out f(a) and f(b).
- Subtract to get the change in output.
- Subtract to get the change in input.
- Divide output change by input change.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsf(x) = −x². Average rate of change on [1, 3]?
AnswerDoes a positive average rate of change guarantee the function increased throughout the interval?
- No. It compares only the endpoints.
- Yes.
The Interval
For f(x) = x², what is the average rate of change on [1, 4]?
AnswerReading It Off the Graph
The secant shown joins x = −2 and x = 3 on y = x² − 4. What is its slope?
The secant between the two marked points. - Point(-2, 0)
- Second point(3, 5)
- Slope between them1
abcFirst pointSecond pointAnswer