COALITION MATH 151, FALL 1997

        Group II (S. A. Fulling, assisted by Cary Lasher)

                             Day 3.3


    1.  Feedback on the function-definition essays
    
        A.  A function is not an "equation" or "statement".
    
        B.  Good statements of vertical line test or uniqueness 
        of y.

        C.  Invitation:  Visit me as a team to discuss your 
        teaming process and get detailed critique of essays.

    2.  Definition of the derivative

        A.  Show slides of secant and tangent lines with 
        increments.

        B.  Offer to derive d(x^4)/dx.
OFFER ACCEPTED.

        C.  Try a more exotic function:  d(a^x)/dx.  Resort to an 
        oracle for lim_{h->0} (e^h - 1)/h:  Maple and/or p. 355 
        of Stewart.

    3. Activity:  Sketch the secant-tangent-increment picture for 
    functions of different monotonicity & concavity.  (Divide 
    teams mod 3.  Call on one team to show on projector.)  (5 min) 
GOT TWO GOOD SKETCHES AND ONE MEDIOCRE ONE.  USED WHITEBOARD 
INSTEAD OF PROJECTOR, DID ALL THREE CASES.
    OUT OF TIME AT THIS POINT.  DID ACTIVITY 4 NEXT TIME.

    4.  Activity:  Given a function, sketch the derivative.  
    (Draw a graph at random on the projector.)  Show results of 
    several teams on projector.  (5 min) 
THIS WENT WELL (ON DAY 4.1).  USED WHITEBOARD.  ASKED FOR AN 
ANTIDERIVATIVE AS WELL.

    5.  Collect papers from both activities and "grade on 
    completion".  
WE RECORDED ACTIVITY 3 BUT NOT 4.