Section 1.1: Rates of Change and the Slope of a Curve (eBook p. 4  8)
Key Concepts:
 Average rate of change refers to the rate of change of a function over an interval. It corresponds to the
slope of the secant connecting the two endpoints of the interval.
 Instantaneous rate of change refers to the rate of change at a specific point. It corresponds to the slope
of the tangent passing through a single point, or tangent point, on the graph of a function.
 An estimate of the instantaneous rate of change can be obtained by calculating the average rate of
change over the smallest interval for which data are available. An estimate of the instantaneous rate of
change can also be determined using the slope of a tangent sketched on a graph. However, both methods
are limited by the accuracy of the data or the accuracy of the sketch.
 Average rate of change refers to the rate of change of a function over an interval. It corresponds to the
slope of the secant connecting the two endpoints of the interval.
 Instantaneous rate of change refers to the rate of change at a specific point. It corresponds to the slope
of the tangent passing through a single point, or tangent point, on the graph of a function.
 An estimate of the instantaneous rate of change can be obtained by calculating the average rate of
change over the smallest interval for which data are available. An estimate of the instantaneous rate of
change can also be determined using the slope of a tangent sketched on a graph. However, both methods
are limited by the accuracy of the data or the accuracy of the sketch.
Prior Knowledge:
 Login at OERB first before clicking the weblink below for the video (Userid: tdsbstudent; Password: tdsb)
Rate of Change (a video reviewing several general concepts related to rate of change)
Lessons for Section 1.1:
Rates of Change and the Slope of a Curve
Part One

Part Two

Average Rate of Change
1. Slopes of Secants and Average Rate of Change
2. Average Velocity (Common example of "average rate of change")
3. Average Rate of Change Given a Table of Values (Example 1)
4. Average Rate of Change Given a Table of Values (Example 2)
5. Average Rate of Change Given an Equation (Example 3)
6. Average Rate of Change Given a Graph (Example 4)
3. Average Rate of Change Given a Table of Values (Example 1)
4. Average Rate of Change Given a Table of Values (Example 2)
5. Average Rate of Change Given an Equation (Example 3)
6. Average Rate of Change Given a Graph (Example 4)
Instantaneous Rate of Change
1. Slopes of Tangents and Instantaneous Rate of Change
2. Slope of a Tangent to a Curve  Numerical Approach (a lesson on finding rates of change numerically)
3. Instantaneous Velocity (Common example of "instantaneous rate of change")
4. Instantaneous Rate of Change Given a Table of Values (Example 1)
5. Instantaneous Rate of Change Given a Table of Values (Example 2)
6. Instantaneous Rate of Change Given an Equation (Example 3)
7. Instantaneous Rate of Change Given a Graph (Example 4)
3. Instantaneous Velocity (Common example of "instantaneous rate of change")
4. Instantaneous Rate of Change Given a Table of Values (Example 1)
5. Instantaneous Rate of Change Given a Table of Values (Example 2)
6. Instantaneous Rate of Change Given an Equation (Example 3)
7. Instantaneous Rate of Change Given a Graph (Example 4)
Average vs. Instantaneous Rate of Change
Assigned Practices:
 eBook: Read p. 6 to 8
 eBook: Do exercises on p. 9 #1 to 9, #11 to 12