Instantaneous Rate of Change

Guided Notes for this lecture

In this section we want to find a way to find the rate of change of a function that is more accurate than the average rate of change. We do this by considering how a function is changing at one point, instead of between two points.

If we have a table of data we can still make good approximations of how our function may be changing at a single point.

When calculus was first discovered there was controversy surrounding who discovered it first, Newton or Leibniz, so we end up with two sets of notation for derivatives. This videos considers the notation we will use going forward.

Finally we look at some ways this is applied with a set of relevant examples.

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

1. What are the key differences between average rate of change and instantaneous rate of change?
2. When we determine an instantaneous rate of change value, what does that tell us?
3. How does the idea of closeness from our limits section work in conjunction with approximating the instantaneous rate of change?

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