Time and Date Stamps (logged): 12:34:21 05-21-2012
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Precalculus II
Calculus I Test 2
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
- Write on ONE SIDE of paper only
- If a distance student be sure to email
instructor after taking the test in order to request results.
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
Using the first-derivative test determine the coordinates of the extreme point
of the function y = -1.221 x ^ 2 + -2.3 x + 29.82, and determine whether this point is a maximum or
a minimum.
Use a second-derivative test to confirm whether this point is a maximum or a
minimum.
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Problem Number 2
The first derivative of a polynomial has exactly one relative maximum and one
relative minimum, and these are the only critical points of the first derivative function.
- Sketch a possible graph of the polynomial, of its first derivative function and
of its second derivative function.
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Problem Number 3
The average value of f(x) = A x^2 between x = 5 and x = 7 is 10. What is the value of
A?
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Problem Number 4
Problem: Obtain a quadratic depth vs. clock time model if depths of 85.007 cm, 74.07 cm and
67.18901 cm are observed clock times t = 8.510502, 17.021 and 25.53151 seconds.
Problem: The quadratic depth vs. clock time model corresponding to depths of 85.007 cm,
74.07 cm and 67.18901 cm at clock times t = 8.510502, 17.021 and 25.53151 seconds is depth(t) = .028 t2
+ -2 t + 100.
- Show the system of equations we would solve to get this model.
- According to the model, what is the precise rate of depth change at clock
time t = 3.4 seconds?
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Problem Number 5
The length of a certain rectangle is changing at a constant rate of .32 cm /
second. Its width is changing at a constant rate of .11 cm/sec.
At t = 0 the length of the rectangle is 28 cm and its width is 10 cm.
- What linear function models the length as a function of time?
- What linear function models the width as a function of clock time?
- Use these two functions and the product rule to determine the area function and
the rate at which area changes at t = 0.
- Use the product rule to determine the symbolically area function and the rate at
which area changes at t = 0 if length is L0 + r1 * t and width is W0 + r2 * t.
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Problem Number 6
At clock time t the voltage in a certain circuit is V(t) = 6 sin ( 170 `pi t) +
6.
- Find the function which gives the rate of change of the voltage at clock time t.
- What is the maximum rate at which the voltage is changing?
- Is the voltage ever zero?
- Is the rate of voltage change ever zero?
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Problem Number 7
What are the signs of f(x) and f ' (x) if the function f is negative and
decreasing at a decreasing rate? Sketch possible graphs of f(x) and f ' (x).
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Problem Number 8
The depth of water in a certain nonuniform container is y = .02 t4 + -2.6 t2
+ 89, where depth y is in cm when clock time t is in seconds.
- At what average rate is the depth of water changing between clock times t = 17.2 and t =
17.3 seconds?
- At what average rate is the depth of water changing between clock times t = 17.2 and t =
17.21 seconds?
- At what average rate is the depth of water changing between clock times t = 17.2 and t =
17.201 seconds?
- What do you estimate is the rate at which water depth is changing at clock time t = 17.2
seconds?
The rate at which water flows from a certain nonuniform cylinder is given by rate = .02
t3 + -2.6 t cm3 per minute, where t is in minutes. How much do
water do you think will flow between clock times t = 17.3 minutes and t = 34.4 minutes?