MAT 1330, Fall 2010 Assignment 5
Due Wednesday November 17, at the beginning of class.
Late assignments will not be accepted; nor will unstapled assignments.
Instructor (circle one): Frithjof Lutscher
Angelika Welte
Aziz Khanchi
Robert Smith?
DGD (circle one): 1
2
3
4
Student Name
Student Number
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Question 1.
For each of the following functions
f
, ±nd the critical points and classify
them; that is ±nd out whether they are local minima, local maxima or neither. Factorize the
derivatives.
a)
f
(
x
)=
−
2
3
x
3
−
7
x
2
−
24
x
+14
Give
f
!
(
x
−
2(
x
+ 4)(
x
+3)
.
Hence, the critical points of
f
are
x
1
and
x
2
(with
x
1
<x
2
)
x
1
=
−
4
and
x
2
=
−
3
.
First Method:
Calculate
f
!
(
x
−
4
x
−
14
.
Find
f
!
(
x
1
2
.I
s
x
1
a max or a min?
Min
FInd
f
!
(
x
2
−
2
s
x
2
a max or a min?
Max
Second method:
x
−∞
x
1
x
2
+
∞
f
!
(
x
)
–
0
+
0
–
f
(
x
)
#
$
#
According to the table: Is
x
1
a max or a min?
Min
Is
x
2
a max or a min?
Max
b)
f
(
x
)=3
−
16
−
8
x

. Write the function as
f
(
x
!
−
13+8
x
if
x<
2,
19
−
8
x
if
x>
2.
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 Fall '08
 DUMITRISCU
 Derivative, lim, Limit of a function, Convex function

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