Rates of Change

You may find it useful to print out the guided notes to fill in while watching the video.   

In this section we will look at how we begin approximating how a functions changes on average. This builds upon your knowledge of lines and slope. We will also review the difference between constant change and percent change.

Further examples to apply what we have learned about the average rate of change.

One application that is very important with rate of change is the idea of Average Velocity. Determining how quickly the position of an object is changing is an application we use frequently in our work and everyday lives.

As we noted in the previous section, how we describe a functions behavior (increasing, decreasing, positive, negative) is important to convey what is happening within the function. We will now add another set of descriptors to our list which describe the way a function bends. This video descirbes the idea of concavity. If you have not learned about concavity yet, I encourage you to make a handy list of all the terms we are using to describle functions and what they tell us.

For the previous work we have done in this section, we have made an assumption that the change we should use is constant (slope). However, there are times when we want to talk about how a function changes that need to take into account the original value of the function. So this next video reviews when, and how, we would use percentage change.

One of the most important ways we use relative change is to make decisions within the economy. In this last video we will look at how relative change can be used to determine the Elasticity of Demand.

At the end of this section you should be able to answer the following questions:

  1. What does the average rate of change tell us about a function?
  2. When do we use average rate of change versus relative rate of change?
  3. How is concavity different conceptually and computationally from other ways we describe functions?

Check Your Understanding
You should try these problems before reviewing the solutions to to these non-graded practice problems.