Rates of Change

  Learning Outcome/Performance Criteria:

1. Compute and interpret average rates of change and their limits. Some of this material is not covered particularly well in the textbook. You should refer to the Average Rates of Change Handout.
   
   
   1. Determine an average rate of change numerically.
      
      • Examples: Handout: Examples 1 and 2
        
      • Videos:
        • My Video
        • Web Video 1 This is a nice video. The part of it for this criterion ends at 2:30, but after that it goes on to the next criterion.
        • Web Video 2 This is a bit slow, but pretty clear.
      • Additional Exercises: Handout: Exercises 1-3
        
      
      
   2. Determine the average rate of change of a function from its graph. Draw a secant line whose slope represents the average rate of change between two points.
      
      • Examples: Handout: Example 4
        
      • Videos:
        • My Video
        • Web Video 1 The part of this video from 2:30 on addresses this criterion for an applied problem. It is probably best to watch the whole thing.
        • Web Video 2 This video finds the average rate of change for the graph of a general function f(x).
      • Additional Exercises: Handout: Exercises 5, 6, 4, 15
        
      
      
   3. Determine the average rate of change of a function algebraically, from its equation.
      
      • Examples: Handout: Example 3
        
      • Videos:
        • My Video
        • Web Video 1 A nice video.
        • Web Video 2 Another good video, showing how to find the average rate of change for a general function f(x).
        • Web Video 3 Another good video, except the way the calculator is used. Just find y for the given x value, using the equation.
      • Book Exercises:
        
      • Additional Exercises: Handout: Exercises 8, 14, 16, 19, 20
        
      
      
   4. Find and simplify a difference quotient.
      • Examples: Handout: Examples 5 and 6
        
      • Videos:
        • Web Video 1 This is a good introduction to where the difference quotient comes from. The camera angle is a bit awkward, but otherwise it is good.
        • Web Video 2 This is a nice video, showing a sequence of more and more (but still not very) complicated examples using the difference quotient.
        • Web Video 3 This video and the next one are good if you feel you need to see more of about the same difficulty as Video 2. Move on to Video 5 if you feel ready to move to somewhat more complicated examples.
        • Web Video 4
        • Web Video 5 And some yet more complicated examples. This includes the function f(x)=1/x.
        • Web Video 6 This shows the computation of the difference quotient for the square root function.
      • Book Exercises:
        
      • Additional Exercises: Handout: Exercises 10 - 13 You could also watch the start of Videos 3 and 4, pause the video after you see the problem, and try working it yourself. Then Play the videos to see how you did.
        
      
      
   5. Approximate an instantaneous rate of change of a function at a point using a sequence of average rates of change.
      
      • Examples: Book Section 2.1: Examples 1 and 2 (pages 61-63)
        
      • Book Exercises: 2.1: 1, 7
        
      
      
   6. Approximate an instantaneous rate of change from a graph, indicating the tangent line used to do it.
      
      • Videos:
        • My Video
      • Book Exercises: 2.1: 9(a), 20(b)
        
      
      
   7. Compare rates of change (average and instantaneous) of a function at various points, from a graph.
      
      • Book Exercises: 2.1: 22, 24, 25
        
      
      
   
   

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