APPM 2350
EXAM 2
FALL 2007
INSTRUCTIONS:
Computers, calculators, books, and crib sheets are not permitted.
Write your (1)
name, (2) instructor’s name, and (3) recitation number on the front of your bluebook. Work all problems.
Show your work clearly. Note that a correct answer with incorrect or no supporting work may receive no
credit, while an incorrect answer with relevant work may receive partial credit.
1. (20 points) Using an appropriate technique from Calculus III, determine the extreme values of the
function
f
(
x, y
) =
x
2
+
y
2
4
, assuming that
xy
= 1. For each point you find, be sure to state whether
the function has a local maxima or minima at that location, and the value of
f
(
x, y
).
2. (20 points) The surface elevation,
z
, of a small mountain area that you have just purchased is given
by the function
z
=

y
2

x
4
+ 4
x
2
+ 54 for

3
≤
x
≤
3 and

3
≤
y
≤
3.
(a) Where on this property would you build a hut? (Hint: perhaps a level spot that is not a summit.
Clearly explain your reasoning, and show your calculations, to support your answer.)
(b) A stream emerges from a spot on the surface located at
P
0
(0
,
1
,
53) and flows downhill following
the line of steepest descent. At the point
P
0
, in which direction does the stream flow? (Give
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 Fall '07
 ADAMNORRIS
 Approximation, trioxin concentration

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