Which gives the correct speed of a car: speedometer, or sat nav? The speedometer on the car measures the average speed over the last few seconds; whereas sat nav measures the average speed over a given horizontal distance; these can be different.

Let $f(x)$ represent the position of a car along a road at time $x$. The rate of change of $f(x)$ with respect to $x$ is the velocity (speed). Next we consider how to define the instantaneous speed as the limit of average speed over shorter time intervals.