Average Velocity versus Instantaneous

In this demo, you will explore the differences between the slope of a secant (the Average Velocity) and the slope of a tangent line (the Instantaneous Velocity) for a specific point. Move the point around and change the sliders so that the points are closer together. What happens to the secant slope as the points approach one another? How do you relate the difference quotient to the slope? What are you doing when you move the points closer together? What is changing? What do we call what we are doing in mathematical notation? Thanks to Doug Kuhlmann for developing this app!
Pick a new f by typing "f(x)=" and filling in with a function into the input bar. What changes?