M408K Third Exam Review – Day 1
1)
A right circular cylinder (with a bottom and a top) is to be designed to hold 24 cubic inches of
a soft drink and to use a minimum of material in its construction. Find the required
dimensions for the container.
2) A poster is to have a total area of 72
2
in
with 1inch margins at the bottom and sides and a 3
inch margin at the top. What dimensions will give the largest printed area?
3)
Find the coordinates of
P
that maximize the area of the rectangle shown in the figure below.
4)
An outdoor tour guide offers the following rates: $200 per person if 50 people (the minimum
number necessary) go on the tour.
For each additional person, up to a maximum of 80 people,
everyone’s charge is reduced by $2.
It costs $6000 (a fixed cost) plus $32 per person to conduct
the tour.
How many people does it take to maximize the guide’s profit?
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This is a graph of the function
3
( )
2
5
f x
x
x
A)
Use Newton’s Method, starting with the value
0
2
x
, to approximate the root of
()
fx
.
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 Spring '09
 g
 Derivative, right circular cylinder, real root, outdoor tour guide

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