Math 11003
Babenko V.
October 20, 2015
Test 2
Name:____________________________
UID#:___________________________
This is a closed book Test. No books, laptops, or messaging are permitted. NO calculators
are allowed. You have 10 problems, they are equal in weight. The entire exam is worth 15
points. For full credits show all work! Box your answer so it is easy to locate. You have
60 minutes.
GOOD LUCK!!!
1
1. Use the sign diagram for
f’
f”(x)
to determine the following.
---
4
a) the critical values of
)I
7
(x)
c{,fr4
b) intervals on which f(x) increases
zjX
c) intervals on which f(x) decreases
d) x-values at which relative maxima occur
e) £-values at which relative minima occur
1
2
x
2
X
0
\I
1
II
5
\J
I
—
?<.
—km
Go
“
Go
03
C
CD
CD
CD
0
CD
CD
CD
C
C
CD
CD
C
CD
I
CD
CD
CD
CD
.
CD
0
fi
/
I
-
-
(_‘
N
7
\
1--
—.
CD
CD
CD
CD
CD
11
1<
‘I
I
II
0
j)
?<
CD
CI)
CD
Z!.-
I
‘I
cc
+
03
II
4. Let y = 2
—3x Find the relative maxima, relative minima, and points of inflection.
3
4x
.
Sketch the graph of the function.
.1_3.2= 16)
L2Y—L
_=-_)
X=-c7
=0
c4
0
ce&.
c4aX.
\Mv\.
\Ia’
“2’-I
•DI/
/4,
-=)
Q
5. An inferior product with a large advertising budget sells well when it is introduced,
but sales fall as people discontinue use of the product. Suppose that the weekly sales S
arc given by
400t
2
(t+7)
—
where S is in millions of dollars and t is in weeks. After how many weeks will sales be
maximized?
/
-
—
4
Cr*r)
-;==-:;
t
wo
4
C-’v
6. Find the absolute maxima and minima for f(x) on the interval [a, b}.
x
x+5,
2
+
3
f(x)=x
—
Sx2x-I
2ik2
-2±-f
_>
,2.
[—2,0]
3
=Y
Xa1
_+2
(-2k
7. Suppose that the daily sales (in dollars) t days after the end of an advertisiig
campaign are given by
S=1200+ t>0.
,
2
t+1
0. decrease for all t > 0, or change direction at some point?
—
Does S increase for all t
-
-
<0
4Q
5
8. If the total cost function for produciiig x lamps is
C(x)
2
3200 ± 32x + 0.5x
dollars. producing how rnaiiv units will result in a minimum average cost. per unit?
-22-- o
j(>c
-32
Zc
LO
s 2O
O
\f\f
A
6
9. Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular
lot and then putting a fence across its middle. If each lot is to contain 1200 square feet,
what is the minimum amount of fence needed to enclose the lots (include the fence across
the middle)?
\
2ccD
T
C
-
-GQQ
\()
--Lko
-=
=21-tO
7
10. a) For the function, find any horizontal and vertical asymptotes.
9x +4
x-2
h) Use information from the first rcrivative to sketch the graph.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
‘=2
;)
Ac-\
Total
3ç-
<0
1’
c)
)
2
8
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/ 100
/15
-