Average Rates Versus Instantaneous Rates
From these labs I have learned about the differences between instantaneous rates and average rates. The second lab shows us about what can be inaccurate about taking an average rate over a large interval. As we take the average rate over a smaller and smaller interval, it becomes closer to describing the behavior of the graph at a specific point. This helps to make sense of the explanation of a deriative as the limit of the average rate as delta x approaches zero. Theses activities also helped to explain more about derivatives in that they are postive when the graph is increasing, negative when the graph is decreasing, and zero at maximums and minimums (or in some cases not), which will help to describe the behavior of a graph without a visual representation.
October 11th, 2006 at 2:12 pm
Try to think of what the graph of the derivative would like for a linear function, a quadratic function, a cubic etc.
Mrs. E