Distance and Accumulated Change

Guided Notes for this lecture

In this chapter we consider what information we can analyze if we START with the derivative instead of finding the derivative. We begin this work with the idea of distance and build from there.

Let's practice some more examples.

Now let's consider how we would approach this if we had data for the derivative instead of algebraic functions.

We need to make sure that we understand all the notation used to discuss the idea of area under the curve.

Let's put together the notation and analysis and try some examples.

Finally, we want to make our approximation as good and accurate as possible. In order to do this we introduce the notation and general approach at area under the curve through Riemann Sums.

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

1. What can the derivative of a function tell us about the original function?
2. How do we use area under the curve to tell us about total change?
3. How can we make our approximation as accurate as possible?

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