Section 3.8 Worksheet:

Assigned problems: Exercises pp. 196-198, #1-4, 9, 14, 22, 42, 46, 51, 57 (due Thursday).

  1. Does the second derivative pose any new challenges from the perspective of the mechanics of differentiation? Why or why not?

  2. 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?

  3. How many times can you differentiate an tex2html_wrap_inline104 degree polynomial before it ``disappears'' (i.e. becomes identically equal to zero)?

  4. How many times must you differentiate the function tex2html_wrap_inline106 before one of its higher derivatives is again equal to tex2html_wrap_inline106 ? Demonstrate.

  5. What is the factorial function? What is its domain?


LONG ANDREW E
Fri Sep 21 11:12:20 EDT 2001