AP Calculus

These labs further differentiated between instantaneous rate of change (derivative) and average rate of change. The gsp lab illustrated using a tangent line how the slope of the derivative increases as the function increases and decreases as the function decreases. This is especially helpful in cases where we are not able to graph the function and need to describe the functions behavior at a particular point. It also showed how the high and low points of a function would have a derivative of 0 because it is neither going up or down. However this is also true for example for a cubic graph when the function is y=x^3 when x=0 the derivative is also 0.

            The second lab further demonstrated how average velocity can be misleading as a variety of different graphs all very different had the same average velocity. It also showed me how inaccurate average velocity is sometimes. It also showed me how when we take the average rate of a function getting closer to the limit the more accurate and closer it is to the derivative (instantaneous rate of a point). It also illustrated how much more accurate a derivative is versus the average rate in discussing the behavior of a function at a particular point. It also made it much clearer of what a derivative is: the behavior of the graph (slope) of a function at a particular point and its connection with the change in x as it becomes more accurate as the change in x approaches 0.

**Also here is what the hw is for tonight:

all Q’s, page 81 1, 2, 3-19 odd, 20. Also fill out what you learned from the two activities on the Blog.

**my scribe post will be up first thing in the morning because i need to use the school computers so i can put in the equation editor thing it won’t let me on the pc**

-Laurie

This entry was posted on Wednesday, October 11th, 2006 at 7:12 pm and is filed under Class Discussions and You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.