rabbani (tar547) – Homework10 – Fouli – (58395)
1
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17
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001
10.0 points
Determine the increasing and decreasing
properties of the function
f
(
x
) = (
x

1)
4
5
(
x
+ 2)
1
5
on its natural domain.
1.
inc: [

7
5
,
1]
,
dec: [

2
,

7
5
]
∪
[1
,
∞
)
2.
inc: [

2
,

7
5
]
,
dec: [

7
5
,
∞
)
3.
inc: (
∞
,

7
5
]
∪
[1
,
∞
)
,
dec: [

7
5
,
1]
4.
inc: (
∞
,

2]
∪
[1
,
∞
)
,
dec: [

2
,
1]
5.
inc: [

2
,

7
5
]
∪
[1
,
∞
)
,
dec: [

7
5
,
1]
002
10.0 points
Find all values of
x
at which the graph of
y
=
x
2

4 cos
x
changes concavity on (

π/
2
, π/
2).
1.
x
=

π
3
,
π
3
2.
x
=
π
6
3.
x
=

π
6
,
π
6
4.
there are no values of
x
5.
x
=

π
3
6.
x
=
π
3
7.
x
=

π
6
003
10.0 points
Let
f
be the function defined by
f
(
x
) =
x

cos 2
x,

π
≤
x
≤
π .
Determine all interval(s) on which
f
is de
creasing.
1.
[

π
6
,

π
12
]
,
[
π
6
,
11
π
12
]
2.
[

5
π
12
,

π
6
]
,
[
π
6
,
11
π
12
]
3.
[

π,

5
π
12
]
,
[
7
π
12
, π
]
4.
[

5
π
12
,

π
12
]
,
[
7
π
12
,
11
π
12
]
5.
[

5
π
12
,

π
8
]
,
[
3
π
8
,
11
π
12
]
004
(part 1 of 2) 10.0 points
Let
f
be the function defined by
f
(
x
) =
x
parenleftBig
2 +
1
3
x
2

1
5
x
4
parenrightBig
.
(i) Determine the derivative of
f
.
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 Fall '08
 JOUVE
 Calculus, local maximum, Rabbani

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