MAT 1330, Fall 2011 Assignment 5
Due WED Nov 16, 8:30am at the beginning of class.
Late assignments will
not
be accepted;
nor
will unstapled assignments.
Instructor (circle one): Jason Levy
Robert Smith?
Olga Vassilieva
Catalin Rada
DGD (circle one): 1
2
3
4
Student Name
Student Number
By signing below, you declare that this work was your own and that you have not copied from
any other individual or other source.
Signature
Question 1.
Consider the function
f
(
x
) =
x

4
x
2
. Follow these steps to graph the function.
(a) The domain of
f
is
x
6
= 0
(b) The
x
intercept(s) of
f
are
f
(
x
) = 0
⇒
x

4 = 0
⇒
x
= 4
(c) The derivative of
f
is
f
0
=
f
0
(
x
) =
x
2
(1)

(
x

4)(2
x
)
x
4
=
x
(8

x
)
x
4
=
8

x
x
3
(d) The critical point(s) of
f
are
f
0
(
x
) = 0
⇒
8

x
= 0
⇒
x
= 8
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
(e) The second derivative of
f
is
f
00
=
f
00
(
x
) =
x
3
(

1)

(8

x
)3
x
2
x
6
=
2(
x

12)
x
4
(f) The point(s) of inflection are
Since
f
00
(
x
)
<
0 for
x <
12 and
f
00
(
x
)
>
0 for
x >
12
⇒
12 is the only inflection point
(g) Find
lim
x
→
0
+
f
(
x
) =
∞
,
lim
x
→
0

f
(
x
) =
∞
(h) Find lim
x
→∞
f
(
x
) =
0
,lim
x
→∞
f
(
x
) =
0
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 DUMITRISCU
 Calculus, Derivative, Catalin Rada, Olga Vassilieva

Click to edit the document details