Math 165
Special Assignment #2
Lowman
Spring 2010
1. For some
f
(
x
)
,
f
0
(
x
) =
x
2
+2
x

8
. Find where
f
(
x
)
is increasing and where it is decreasing.
2. For some
f
(
x
)
,
f
0
(
x
) =
x
2
+ 2
x

8
. Find where
f
(
x
)
is concave up and and where it is
concave down.
3. For some
f
(
x
)
,
f
0
(
x
) =

10
x
2
+ 60
x

50
. Find the
x
coordinates of all first order critical
points and use the first derivative test to determine what kind of critical point at each x.
4. For some
f
(
x
)
,
f
0
(
x
) =

10
x
2
+ 60
x

50
. Find the
x
coordinates of all first order critical
points and use the second derivative test to determine what kind of critical point at each x.
5. Given
f
(
x
) = (
x
2
+ 7
x
+ 1)
·
p
5
x
2
+
x
)
find
df
dx
at
x
= 1
.
6. A company estimates that the cost in dollars of producing
x
units of a certain product is
C
(
x
) =
x
2
5
+ 6
x
+ 1000
. Find the production level that minimizes average cost. Hint: find
average cost, find all critical numbers for average cost, use the first or 2nd derivative test to
determine that the CNs correspond to a minimum.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 STAFF
 Math, Calculus, Derivative, $2, Lowman, Convex function, $1.00

Click to edit the document details