he average daily temperature (in ◦ Fahrenheit) in Portland, Maine is given by A(t) where t is the number of days after January 20. Furthermore the price of oil required to heat a home, O (measured in dollars per gallon) depends on the average daily temperature, A. (a) What is the meaning of O(A(0)) = 3.2 in the context of the problem? Be sure to include the units. (b) What is the meaning of dO dA ∣∣A=10 = −0.02 in the
he average daily temperature (in ◦ Fahrenheit) in Portland,
Maine is given by A(t) where t is the number of days after January 20. Furthermore the price of oil
required to heat a home, O (measured in dollars per gallon) depends on the average daily temperature,
A.
(a) What is the meaning of O(A(0)) = 3.2 in the context of the problem? Be sure to include the
units.
(b) What is the meaning of dO
dA
∣∣A=10 = −0.02 in the context of the problem? Be sure to include the
units.
(c) What is the meaning of dO
dt in the context of the problem? What are the units?
(d) Recall from Written Homework 1 that the price of oil varied linearly with average daily temper-
ature where O(A(t)) = −0.02A(t) + 3.5. Compute dO
dt . (Your answer may contain A and its
derivative.)
(e) Now recall that the average daily temperature varied sinusoidally over time so that A(t) = 46 −
36 cos
(2π
365 t
)
. Compute dO
dt .
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