Secant Line and AROC
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Lesson Summary:
Learn how to calculate the average rate of change of a function by finding the slope of a secant line that connects two points on the graph. This line represents the equivalent trip taken at a constant average velocity, and its slope corresponds to the function's overall average rate of change over the given interval. By understanding this connection between secant lines and average rate of change, you can more easily interpret and analyze the behavior of functions on a Cartesian plot.
Lesson Description:
Be able to explain how average rate of change of a function corresponds to the secant line on a Cartesian plot of that function.
Check out www.themathdude.org for more videos.
Additional Resources:
- Secant Line - Explanation and picture of what a secant line is
- Secant Java Applet - Interactive secant and tangent line Java applet
- Another Secant Line Applet - Another secant java applet where you can control the interval
- Last Secant Line Applet - One more secant java applet where you can specify the function
- Speed and Acceleration in Business Notes - Notes about speed and acceleration in business
- Speed and Acceleration in Business Problem Set - Problem set about speed and acceleration in business
- Linear Approximate Rate Notes - Notes about linear approximations of rates
- Acceleration a Formula - Function - Mini Project - Mini Project about Estimating Future Sales â From Function to Equation to Formula
- Linear Extrapolation Notes - Notes about linear extrapolation
- Linear Extrapolation Problem Set Solutions - Solutions to the Linear Extrapolation problem set
Questions answered by this video:
- What is a secant line?
- What is AROC or average rate of change and how do you find it?
- How do you draw an average rate of change line for a curve?
- How do you find the slope of the secant line from the beginning to the end of a curve?
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Staff Review
This lesson explains average rate of change from the beginning to the end of a time period for the graph of a relation. The average rate of change graph is a line with constant velocity or slope. This concept is explained very well and has many different resources to supplement the video.
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