Here are the main points that will be addressed in the videos. Please read these and think about them as you watch.

  • When explaining the meaning of in context:
    • Using “instantaneous rate” can be accurate but often does NOT convey much meaning.
    • If rate is NOT constant, then it need NOT be true that for any one unit change in the independent quantity (input), the dependent quantity (output) changes by units.
    • If is differentiable at , then there is a sufficiently small amount of change in the independent quantity (input) from where the graph of is indistinguishable from a line.
    • So means that as the independent quantity (input) varies by a sufficiently small amount from , the change in amount of the dependent quantity (output) from is essentially times as much as the change in the independent quantity.