Math 142
Exam 2 VERSION A
March 21, 1997
Name
Roster Number
Section
SEAT
M.C.
1
2
TOTAL
The work on this exam is my own
(signature required)
Please read all directions. Be sure any written work to be read by me is legible. There are 2 pages
with writing on both sides of every page. When you are done, turn in your exam and your scantron
in the appropriate envelope. There is a ve point deduction for any error in your name, roster
number, section number, version letter (on your scantron) or missing signature. There is a 10 point
deduction if I have to grade the scantron by hand.
This exam is copyright c 1997 by Janice Epstein. No part of this exam may be reproduced without
the author's express written consent.
Math 142
2
Exam 2A
PUT YOUR NAME AND VERSION LETTER (A) ON YOUR SCANTRON! There are 15 multiple
choice questions to answer on your scantron. There is no partial credit on this part. The scantrons
will not be returned, so please mark you answers on the exam too.
1. Given the equation of motion, ( ) = ,10 2 + 40 + 5 where is in meters and is in seconds,
nd the average velocity from = 2 to = 3.
s t
t
(A) -10 m/s
t
t
s
t
t
(B) 10 m/s
(C) 40 m/s
(D) -40 m/s
(E) none of the above
2. Arrange the points A, B and C in order of increasing slope of the tangent line.
(A) ABC (B) BCA (C) CBA (D) CAB (E) none of the above
3. Which of the equations below is the derivative of ( ) = 2 2 ?
f x
2(x + h)2 , 2x2 (B) lim 2(x2 + h) , 2x2
(A) lim
!0
!0
h
h
x
x
2(x2 + h2 ) , 2x2 (D) lim 2(x + h)2 , 2x2
(C) lim
!0
!0
h
h
h
h
h
(E) none of the above
4. Given the graph of 0( )(=DF/DX), nd the
graph of ( ). All graphs are on the same window
settings.
F
x
F x
(A)
(B)
(C)
(D)
(E) none of the above
p
5. Use the tangent line approximation to nd the approximate change in ( ) = 2 , as
changes from 4 to 4.5.
p x
(A) -3/8
(B) -.2574
6. Given ( ) =
f x
(A)
x
e
1
+ ,
e
x
e
x
(C) -1/2
1 , nd 0( ) =
+ ,
(B) ,1 ,
(C)
e
f
x
x
e
e
x
(D) -1/4
x
x
x
(E) none of the above
x
,1
x
e
x
+ ,
e
,
(D) (, ++ , )2
x
e
x
e
e
e
x
x
(E) None of the above
Math 142
3
+ 1 , nd 0( ) =
7. Given ( ) = ,
2
(A) 1 2
(B) 3 2
( , 2)
( , 2)
x
f x
f
x
x
x
(C) 1
x
8. Given ( ) =
f x
2
x
e
x
(D)
,3
( , 2)2
(D)
x e
x
(E)
,1
( , 2)2
x
, nd 00( ) =
f
x
(A) 2 2 (1 + 2 2) (B) 4
e
Exam 2A
(C)
2
x
x
xe
2
x
e
2
(E) 2
2
x
2
x
xe
9. Given ( ) = j 3 + 1j, nd 0( ) =
f x
ln x
(A) j 3 + 1j
f
x
(B) ( 3 + 1),1
ln x
(C) 3 2( 3 + 1),1 (D) 3
x
x
x
(E) 3
2
x
2
j 3 + 1j
x ln x
10. Find the slope of the line tangent to ( ) = (3 + )2 3 at = ,2
f x
(A) .6667
(B) 2/3
x
(C) 1
Problems 11 and 12 use the cost function ( ) = 2
11. What is the marginal cost?
C x
(A) 5
x
(B) 2
1:5
=
2:5
x
+ 100
2:5
x
(C) 2
2:5
x
x
(D) 1/2
(E) none of the above
(D) 100
(E) not enough data
+ 100
12. Use the marginal cost to nd the approximate cost to produce the 4th item.
(A) 25.98
(B) 40
(C) 32.82
13. Given the function ( ) =
f x
p
(A) 0 3
(B) 3
;
4
x
(D) 100
(E) not enough data
, 18 2 + 15, where are the in ection values?
p
(C) 0 3
(D) 3
(E) 0
x
;
14. If thepfunction that models the increase in the biomass of sh over the next year is given by
( ) = 5 , 2 , in hundreds of kilograms, nd how many sh should be kept in the lake to
maximize the increase in the biomass of sh.
x
f x
(A) 625 kg
x
x
(B) 156 kg
(C) 150 kg
(D) 312 kg
(E) none of the above
15. Which of the functions below is the best linear approximation to the function
(A)
x
e
(B) 1 ,
x
(C) 1 +
x
(D) 1 +
x
xe
x
e
near = 0?
(E) 1
x
Math 142
4
Exam 2A
WORK-OUT PROBLEMS (credit as listed).
1. (10 points) Given the information below about the function ( ),
,1
0
1
2
we also know that (0) and 0(2) DNE.
& % % % &
f x
f
^
^
_
Find the following:
(a)
critical values
(b)
in ection values
(c)
relative minima
(d)
relative maxima
^
f
^
(2 bonus points) make a rough sketch of this function:
2. (15 points) Graph the function f (x) = 1 ,x3x .
2
Show on the graph (or list) all intercepts, asymtotes, extrema and in ection points. Find EXACT
values for full credit.