Math 102 Review for Exam #2
Exam Coverage:
Sections 13.113.3, 14.1, 14.2, 15.1
Date:
Wednesday, March 7, 8 am
Rooms
Sections
Main Auditorium
001, 002, 003, 005, 006, 008, 009, 010,
018, 022, 023, 025
Nesbitt 111
004, 011, 013, 017
Nesbitt 125
019, 020
CAT 61
012, 021, 024
Problems:
For problems 1 and 2, make a sign diagram for the first derivative and determine where the function is
increasing and decreasing, any relative extrema, make a sign diagram for the second derivative and
determine where the function is concave up, concave down and any points of inflection:
1.
(
29
3
2
3
9
7
f
x
x
x
x
=


+
2.
(
29
4
3
2
8
18
8
f
x
x
x
x
=
+
+
+
For problems 3 and 4, find the absolute extrema on the given interval:
3.
(
29
3
27
[ 2,2]
f
x
x
x on
=


4.
(
29
2
3
6
[0,5]
f
x
x
x
on
=

5.
The fuel economy (in miles per gallon) of an average American compact car is
(
29
2
.015
1.14
8.3,
E x
x
x
= 
+
+
where x is the driving speed (in miles per hour, 20
60
x
≤
≤
).
At
what speed is the fuel economy the greatest?
6.