Section 3.8 Quiz:
  1. In the context of the physics of the position of a point as a function of time, what is the meaning of the second derivative? the third derivative?

    The second derivative represents the acceleration; the third derivative is the instantaneous rate of change of the acceleration, known as the jerk. When you drive a car you can tell the difference between smooth acceleration and sudden accelerations and deccelerations (caused, as in the case of my old Toyota, by things like the engine cutting out abruptly, etc.). This is related to the rate of change of acceleration, or the jerk.

  2. How many times can you differentiate an nth degree polynomial before it ``disappears'' (i.e. becomes identically equal to zero)?

    The nth derivative of an nth degree polynomial is non-zero, but the (n+1)th is identically equal to zero.