MATH 1100-001
EXAM 2
Instructions:. Put your name on the exam. Show your work for hill credit. Calculators and other electronic
devices (including cell phones) are not allowed. You are allowed one side of an 8.5 by 11 inch sheet of notes.
1. Suppose that the the total cost function is C(c)
1000 + 92r, where r is the number of goods produced,
awl that price per unit is p(r) 1O+ x
(the price at which x goods will sell).
—
-
a. (5 points) Find the revenue function.
bc)=
f/1
(iox—)
/oOx
b. (5 points) Find tlìe marginal revenue, aid marginal cost functions.
1x) /ot
-
Q
0
0
41zx/z
c. (5
points)
qz
Find the profit function.
Pix k-ux
1oO÷x (i)
d. (5 points) Find the marginal profit function.
P
)
R1
/y)
(j
1t
ZX
X
le. (10 points) Find the number of units sold that maximizes the profit.
2x—X
5h
‘
Z—L
ó erV
2. Suppose that the cost for producing r goods is C(a)
=
40 + 0.la’
2
a. (5 points) Find (r), the average cost per unit.
C()
-
-
9o
—
+
i
o—
—
—
+
LI s
b. (20 points) Find the number of units produced that minimizes the average cost per unit. What is the
minimum average cost per unit?
oI —Y 0
1-W
1
(i
C
/X)
0,)
L
_L)
x
)
/
O,.I
xzo.
—
-?)
C/k) Oi
c =t
((yo)
>2
3
LL
4
)‘iI
C1
i)
2
/5
3. Let
f(r)
=
—
22
+ 3x + 2.
a. (5 points) Find the critical values of
f(x).
f(
3
-
(7_3)(Y)
b. (5 points) Find the intervals on winch
f
is increasing and decreasing.
I
x
2
1(
D
d (
(
(i,
1
Q (,14J
1’
—
‘3
c. (10 poiits) Find the relative rnaxiniuin and iniiiimmii points (if any).
1 de’ v h Je,f
ri
f(,’1—23Z
/
/
/
/0/i
3
_ij
d. (10 points) Find the intervals on which
f is concave up aiid concave done,
//
cc
f
X2
1/
F 13)
-
4-
z
6
-
as well as aiiy inflection points.
4. Let
•f
be the function:
—
3 + i
2T
1)
—
a. (5 points) find the domain of
/ç
(A)k
f.
CJL
4R
I
k
Cf’t’b
U
710) /)
I.
b. (5 points) Find the vertical asymptotes (if aiy).
tu
If
)
cypit
k—1
X=-L)
c. (5 poiiits) Find the horizontal asymptotes (if any).
1)’
x
c—’
)G—2Q
2
k
-
lJ