Approach the derivative from a different and more real-lifey
direction. There are two ways to think about speed while
driving. The first way is to look at the speedometer, which
shows how fast the vehicle going at that moment. The other way
is to take the number of miles driven and divide by how long the
drive took. The first way tells the "instantaneous" speed—the
speed at that instant. The second way gives average speed over
the whole trip. Although looking at the speedometer may seem
like the best way to figure out speed, in order to relate this
driving stuff properly to derivatives we need to talk about
average speed first.