Comments for 20:

40 for 3-18b and 20 for each part of 3-19

Average of 64.3, high of 100

3-18b I took off points if a student started in the middle of the proof and
skipped the part done in class, as I was told to do so by Dr. Hassett.
Generally, though, this problem was good.

3-19 was a disaster. Some people gave examples where B=-1, which really doesn't
ruin the spirit of the proof but violates the instructions nonetheless. Some
people did not give any justifications as to why their function is a min or max
or neither, which is basically the point of the problem.

Most students fell victim to a horrible mistake. Several students 
said that if a function attains its minimum or maximum at the origin, then it
has a min or max (respectively) at the origin. By this reasoning, you could
claim that f has a minimum and a maximum at the origin if f is idendically 0.
Students ought to show that within a neighborhood of (0,0) f is strictly
positive (or negative). This is why (x+y)^2 / 2 does not work for part a,
because if y = -x, then f is zero within any neighborhood of (0,0). I dont
mean to dwell on this point but it is a very important one that few people seem
to understand.