The rate of change is fairly easy to understand when moving at a constant speed. It's just distance over time. But what if you are speeding up and slowing down?

No matter how you speed is changing, you can always talk about the average rate of change over a certain time interval. If you cover 37 miles in 60 minutes, we were moving at an average speed of 37 miles/hour. The following video shows how, by averaging over shorter and shorter time periods, we can get the instantaneous rate of change.

Average and instantaneous rates of change are also related to the graph of a function. The average rate of change is the slope of a secant line. That is, the slope of a line between two points on the graph. The instantaneous rate of change is the slope of a tangent line.