Math 215
Homework Set 5:
§§
14.7–15.2
Winter 2012
Most of the following problems are modified versions of the problems from your text book,
Multivariable
Calculus
, 7th ed., by James Stewart. Your solution to each problem should be complete, show all work,
and be written in complete sentences where appropriate. For
Maple
problems, include a printout that
shows all of the work and graphs that you generated in
Maple
to solve the problem, in addition to any
work you may have done by hand.
14.7.3: Consider a function of one variable,
f
(
x
)
, which is continuous on an interval
I
. If
f
has a single
critical point,
x
=
a
, in
I
, then if that point is a local maximum (or minimum) it must also be an
absolute maximum. Explain why this is. Next, consider the function of two variables,
g
(
x, y
) =
3
xe
y

x
3

e
3
y
. Note that this is continuous for all values of
x
and
y
.
(a) Show that
g
(
x, y
)
has a single critical point, and find it.
(b) Show that
g
(
x, y
)
has a local maximum at this point.
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 Winter '08
 Fish
 Calculus, Critical Point, Optimization, lagrange multipliers, local maximum

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