In this second introductory section, we develop the concept of “average rate of change” by considering some further scenarios of everyday motion, and then extend those ideas to define average rate of change for any function. We then consider shorter and shorter intervals over which we compute the function’s average rate of change, giving us better and better estimates for what happens at a particular moment (or any input value) of interest. . . and bump up against a fundamental limitation for how far this approach can take us without developing some new (Calculus!) tools.