Quiz #8 (3.4 & 3.5)
Classlb:
Name: s’
Math 1210 008 Fall 2012
-
October 23, 2012
Score
Instructor: Katrina Johnson
)D—S
-
Instructions: Complete each problem. Show all of your work as partial credit will be given
where appropriate, and there may be NO credit given for problems without supporting
work All answers should be completely simplified, unless otherwise stated. You may NOT
use a calculator. You may use a 3x5 index card.
(10 pts) 1. A box with a square base, rectangular sides, and open top is to contain 6 cubic
feet of space. If the material for the base cost $3 per square foot and the material for
the sides cost $2 per square foot. betermine the dimensions of the box so that the cost
of the materials is minimized. (bon’t forget your units.)
C1
4
r
=
‘coa
C 3x
c\1
.c (
—
-2
((irvl’)
—
-
3+
C(x)
c’
2
-
C’C)()
oE
(=o
3
(2)1
=)
Uç
c-s-
.
-
-
<-SD
.)(3
s
Box bimensions:
(30 pts) 2. For f(x)
Given: f(x)=
=
2(x.- 5)2
,
—50
2
2x
x
2
and
2#.
“.
ç.
2cr,
answer the following questions.
100
f”(x)=—
x.
a) braw the sign line for f’(x)
f
C-)”)
‘>
2co
—
--
-s
ct5
S
b) Find all the local minimum and maximum points, if they exist, or state that they bNE.
rQ..’)(.’
c()..
c’r-.
2(-
oo
-s
Local Max point(s):
..
0
.
—
—
,0)
(CD
Local Mm point(s):
I-D-)
c) braw the sign line for f(x)
II()
DE
‘o
‘
I,
+
—
d) Find all inflection points, if they exist, or state that they bNE.
.l(c)
Inflection point(s);
e) Find the asymptotes, if they exist.
2
-S)
“
0
0
-(%);:
2(<-5):
50
2’ -20,c
-2o-
’A
2
c9::oo
•‘)( \l-’2-
40
—------
c-c,c).
-
r
0
20%
50
Vertical asymptote(s):
A,
‘)(4±o
Horizontal asymptote:
•L%
t±00
4
(Extra Credit) Oblique asymptote:
=
L)
f) Sketch the graph
-20
2
—
20