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
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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
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(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
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- Fall '08
- DUMITRISCU
- Calculus, Derivative, Catalin Rada, Olga Vassilieva
-
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