016A S2 Homework 5 Solution
Jaeyoung Park
*
September 30, 2007
•
2.1 #6
Describe the graph.(See p.150)
Solution
It has a maximum at
a
≈ 
0
.
5 Increasing for
x < a
≈

0
.
5, relative maximum at
x
=
a
≈ 
0
.
5 with maximum value
α
≈
5
.
2. decreasing for
x > a
. Concave down for
x <
3 and inflection point
at
x
= 3, Concave up for 3
< x
.
x
intercept at (

3
.
5
,
0),
y
intercept at
(0
,
5
.
1). (
y
= 0 is an asymptote? Since we don’t have an information
for 8
< x
, this is not clear.
You may say we have an asymptote or
not. Either way should be fine.) (
Every value other than
x
= 3
is an
approximate
)
•
2.1 #8
Describe the graph. (See p.150)
Solution
Increasing for
x <

1, relative maximum at
x
=

1 with
maximum value 5, decreasing for

1
< x < a
≈
2
.
8, relative minimum
at
x
=
a
≈
2
.
8 with minimum value 2. increasing for
a
(
≈
2
.
8)
< x
.
Concave down for
x <
1, inflection point at
x
= 1, concave up for
1
< x
.
x
intercept at (

2
.
4
,
0)
,
(1
.
2
,
0)
,
(4
.
3
,
0) (
approximates
)
y

intercept at (0
,
3
.
3).
•
2.1 #10
Describe the graph. (see. p. 150)
Solution
Increasing for all
x
. no relative maximum or minimum.
Concave down for
x <
3, inflection point at
x
= 3.
Concave up for
3
< x
.
x
intercept at (

.
5
,
0) (
approximate
),
y
intercept at (0
,
1).
Defined for all
x
and no asymptote.
*
jaypark at m a t h . b e r k e l e y . e d u. GSI for 16A 205,211,213
1
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•
2.1 #12
Describe the graph. (see. p. 150)
Solution
Increasing for
x < a
≈ 
1
.
5, relative maximum at
x
=
a
≈ 
1
.
5 with maximum value
≈
3
.
4, decreasing for
a
≈ 
1
.
5
< x <
b
≈
2, relative minimum at
x
=
b
≈
2 with minimum value
≈ 
1
.
5,
increasing for
b
(
≈
2)
< x < c
≈
5
.
5, relative maximum at
x
=
c
≈
5
.
5
with maximum value
≈
3
.
3, decreasing for
c
(
≈
5
.
5)
< x
.
Concave
down for
x <
0, inflection point at (0
,
1), concave up for 0
< x <
4,
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 Math, Critical Point, Derivative, Convex function

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