Math 400
Review
for
Exam 3
Applied Min/Max
1. (20pts) Use calculus min/max techniques to find the dimensions of a rectangle with perimeter
500 ft whose area is as large as possible.
2. (20pts) A 400 meter track consists of two straights and two semicircles of radius r at the end of
each straight. Use calculus min/max techniques to find to find the length of straight L and the
radius of curved end r if the track is to enclose maximum area.
3. For a rectangle with area 100 square feet to have the smallest perimeter, what dimensions
should it have?
4. A packaging company is going to make open topped boxes, with square bases that hold 108
cubic centimeters. What are the dimensions of the box that can be built with the least material?
5. An open rectangular box with square base is to be made from 48 square feet of material. What
dimensions will result in a box with the largest possible volume?
6. A rectangle has its base on the x-axis and its two upper corners on the parabola
What is the largest possible area of the rectangle?
.
Graphing problems
1.
a)
b)
c)
d)
Sketch the graph of a continuous functions that satisfies the following conditions:
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) (
)
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)
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)
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and
2. Sketch the graph of a continuous functions that satisfies the following conditions:
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a)
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b)
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c)
)
3. Sketch the graph of a continuous functions that satisfies the following conditions:
( )
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a)
( )
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b)
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c) ( )
4. Use calculus techniques to sketch each function. Be sure to include and label all local
extrema, points of inflection, intercepts and asymptotes in your graph.
a)
b)
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c)
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d)
(
)
5. Evaluate each limit. Use L’Hopital’s Rule when it applies.
a)
b)
c)
(
)