Math 215
Homework Set 4:
§§
14.5–14.7
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.
14.5.1: Wheat production
W
in a given year depends on the average temperature
T
and the annual rainfall
R
. Scientists estimate that the average temperature is rising at a rate or
0
.
15
◦
C/year and rainfall is
decreasing at a rate of
0
.
2
cm/year. They also estimate that, at current production levels,
∂W/∂T
=

1
and
∂W/∂R
= 5
.
(a) What is the signiﬁcance of the signs of these partial derivatives?
(b) Estimate the current rate of change of wheat production,
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 Winter '12
 NoProfessor
 Calculus, Multivariable Calculus, Vector Calculus, Gradient, level curve, gradient vector, 0.2 cm

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