AP Calculus

Okay, so I realized in class today that the product rule is written u’v +uv’ (in my blog I used capitals- sorry!)

the pdf. files are great but do you guys think that from now on we could write what topics we went over that class as a heading. I think it will make it easier for everyone if they are looking for notes on a specific topic and don’t exactly remember the day we went over [...]

From these labswe did in class I  learned about the many differences in instantaneous rates and average rates.  Ella did a very good job describing the differences and why the labs were helpful. One lab showed showed how inaccurate it is taking an average rate in relation to large interval. The average rate is focused more on the specific behavior of a specific point [...]

I have just completed the labs on instantaneous rate of change and tangents.  I didn’t really learn much from the instantaneous rate of change lab, but it the work on the lab made it clear that the derivative of a point found by the secant line is much more accurate if c is small.  (Given [...]

What I did learn from the exercises
•    I have learnt what the average rate of change between two points on a function looks like. And when one point approaches the other, average rate approaches instantaneous rate. Even more I have learnt what the instantaneous rate look like.
•    A tangent line is a line that interact [...]

The Getting Off on a Tangent lab showed a number of things. It first pointed out that the average rate of change between two points on a function is the slope of the secant line between the two points. Then as one point approaches the other, the average rate approaches the instantaneous rate. [...]

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 [...]

Well ella summed the labs up very well. The first lab helped show me where we will be going, in describing the derivative in a graph and how the derivative is related to the the functution. its poositive when the function increasing, negative when the funtion is decresing, and zero at the appex of curve. [...]

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 [...]

This is a place where I hope we can have rich discussions about problems or concepts etc. It will be what you make it. It’s a great place to discuss mathematical topics that we don’t have time to address in class because of time constraints.