This preview shows page 1. Sign up to view the full content.
ASSIGNMENT 5  SOLUTIONS
Problem 1.
Done in class.
Problem 2.
Take
f
(
x
) =
x
2
, whose graph is a parabola. Drop it by 1 (so now the function is
g
(
x
) =
x
2

1). Slide it to the right by 1 (the function becomes
h
(
x
) = (
x

1)
2

1 =
x
2

2
x
.)
This graph has all the required properties.
Problem 3.
By deﬁnition, concave upwards means increasing ﬁrst derivative. If
f
Í
and
g
Í
are
increasing, then so is their sum
f
Í
+
g
Í
= (
f
+
g
)
Í
. So the ﬁrst statement is true. But the second
is false. For example, both
f
(
x
) =
x
2
and
g
(
x
) =
x
4
+
x
2
are concave upwards on [0
,
1] yet
f
(
x
)

g
(
x
) =

x
4
is concave downwards on [0
,
1].
Problem 4.
To start oﬀ, the domain of
f
(
x
) =
x
√
9

x
is (
∞
,
9].
The ﬁrst derivative is
f
Í
(
x
) =
x
Í
√
9

x
+
x
(
√
9

x
)
Í
=
√
9

x
+
x
1
2
1
√
9

x
(9

x
)
Í
=
√
9

x

x
2
√
9

x
=
2(9

x
)

x
2
√
9

x
=
18

3
x
2
√
9

x
=
3
2
6

x
√
9

x
The critical numbers of
f
(
x
) are
x
= 6 (
f
Í
(6) = 0) and
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/31/2011 for the course MATH 102 taught by Professor Maryamnamazi during the Spring '10 term at University of Victoria.
 Spring '10
 MARYAMNAMAZI
 Calculus, Logic

Click to edit the document details