Once again "the management " is happy to cooperate by supplying a
place where answers ** supplied by students** (along with comments
and corrections, if necessary) will be posted. Students who supply
material for this page will be credited using their initials. So please
send answers, comments, and corrections. Graphs should be described as
well as possible. This isn't supposed to be a complete description of
solutions, but just a place where someone who has attempted the
problems can check their final conclusions.

Problem #1:

a) M(x) -> + infinity as x -> + infinity and M(x) -> - infinity as x
-> - infinity (CREDIT: RE, 12/9/97). Still unanswered: Why does this
"force" M to have at least one real root?

b)

c)

Problem #2:

Problem #3:

a) (7/3)x^3-3e^x + 5 ln(x) + C (CREDIT: anonymous, 12/8/97; thanks to
SS for correcting a sign error, 12/12/97)

b) (1/7)x^7+(10/4)x^4+ 25x + C (CREDIT: anonymous, 12/8/97)

c) -5 cos(x) + (1/5) sin (5x) + C (CREDIT: AG, 12/9/97)

Problem #4: (1/2)x^4 -x -3 (CREDIT: RE, 12/9/97)

Problem #5: The highest point is (1,9/2) so the highest the curve can be is 9/2. The formula for the function used is y=-(9/2)x^2+9x. (CREDIT: IP, 12/12/97, with a partial solution by MG & YC, 12/11/97)

Problem #6:

a) (83)/(24) or 3.458 (CREDIT: anonymous, 12/8/97)

b) 16 (CREDIT: anonymous, 12/8/97)

c) (248)/(27) or 9.185 (CREDIT: anonymous, 12/8/97)

d) - cos(2 Pi) + cos (Pi) = -2 (CREDIT: AG, 12/9/97)

Problem #7:

a) 2e^x sin x (CREDIT: anonymous, 12/8/97)

b) (1/2) e^(Pi) + (1/2) (CREDIT: AG, 12/9/97)

Problem #8:
The answers are 0 and 0 and 0. (CREDIT: MG and YC, 12/11/97)

Remark by the management: the answers reveal a certain dullness in the
questioner (!!). Maybe it would have been better to ask for a value of
the derivative at, say, sqrt(Pi/2) or sqrt(Pi/3) for example. Oh well.

Problem #9:

a)

b)

Problem #10: (63)/6 or 10.5 (CREDIT: anonymous, 12/8/97)

Problem #11: 1/(12) (CREDIT: anonymous, 12/8/97)