MAT 131 Test 3
Fall 1997
Show all work for credit. Do all your work neatly on the paper provided.
Write your name on each sheet you turn in. I will not grade any
work done
on the test sheet. When you are finished turn in all sheets including the
test.
Good Luck.
- 1.
-
A sailor standing on the edge of a dock 15 feet above the lakes
surface is pulling in her boat by means of a line attached to the boats bow.
She pulls in the line at a rate of 5 \fracftsec. How fast is the boat
approaching the foot of the dock when the boat is 20 feet away.
- 2.
-
Given f(x) = x3-12x+10
- a.
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Find the intervals on which f is increasing.
-
b.
-
Find the intervals on which f is decreasing.
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c.
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Find the intervals on which f is concave up.
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d.
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Find the intervals on which f is concave down.
- 3.
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Find all critical points of f(x) = x2-1/x2-x-2.
- 4.
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How many real roots does x3/3-x2/2-2x+1 = 0
have?
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5.
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Find all horizontal and vertical asymptotes of y = x2-4/x2-3x+2.
- 6.
-
Graph f(x) = x2+1/x2-1.
- 7.
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Given g(x) = 1/x2+1, g¢(x) = -2x/(x2+1)2, and
g¢¢(x) = 2(3x2-1)/(x2+1)3 graph g. Please
label all max's/min's and points of inflection.
- 8.
-
A cylindrical tin can is to hold 50 cm3 of fluid. How should
it be constructed in order to minimize the amount of material needed in
its construction? (Note: Tin cans have tops and bottoms)
- 9.
-
Given an example of a function and an interval for which the
mean value theorem does not hold and explain why not.
File translated from TEX by TTH, version 1.58.