We already know that the slope of a function at a particular point is given by the derivative of that function, evaluated at that point. So we can easily find the slope, or the rate of change, in one particular location, and so we could call this the instantaneous rate of change, because it’s the rate of change at that particular instant.

If instead we want to find the rate of change over a larger interval, then we’d need to use the average rate of change formula. After all, we’re looking for the average rate at which the function changes over time, or over this particular interval. To do that, all we need is an equation for the function, and the endpoints of the interval we’re interested in. We can plug those things into the average rate of change formula, and we’ll have the average rate of change over the interval.

So in the same way that the derivative at a point, which we can also call instantaneous rate of change, is equal to the slope of the tangent line at that point, the average rate of change over an interval is equal to the slope of the secant line that connects the endpoints of the interval.

0:27 // Formula for the average rate of change
0:49 // Average rate of change is equal to the slope of the line
1:17 // When average rate of change is negative, positive, and zero
2:30 // Average rate of change vs. instantaneous rate of change
3:12 // Average rate of change from a table

Want to learn more about Derivatives? I have a step-by-step course for that. 😃