rabbani (tar547) – Homework05 – Fouli – (58395)
1
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printout
should
have
15
questions.
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before answering.
001
10.0 points
Find the value of
f
′
(4) when
f
(
x
) =
5
3
x
3
/
2
+ 2
x
1
/
2
.
1.
f
′
(4) =
11
2
correct
2.
f
′
(4) =
13
2
3.
f
′
(4) = 6
4.
f
′
(4) =
15
2
5.
f
′
(4) = 7
Explanation:
Since
d
dx
x
r
=
rx
r
−
1
,
we see that
f
′
(
x
) =
5
2
x
1
/
2
+
x
−
1
/
2
.
At
x
= 4, therefore,
f
′
(4) =
11
2
.
002
10.0 points
Determine the derivative of
f
when
f
(
x
) =
parenleftbigg
2
3
parenrightbigg
2
/
3
.
1.
f
′
(
x
) = 0
correct
2.
f
′
(
x
) =
4
9
x
−
1
/
3
3.
f
′
(
x
) does not exist
4.
f
′
(
x
) =
parenleftbigg
2
3
parenrightbigg
x
−
1
/
3
5.
f
′
(
x
) =
2
3
parenleftbigg
2
3
parenrightbigg
−
1
/
3
Explanation:
The derivative of any constant function is
zero. Consequently,
f
′
(
x
) = 0
.
003
10.0 points
Find the value of
f
′
(
−
1) when
f
(
x
) = 2
x
3
−
7
x
−
2
−
5
.
Correct answer:
−
8.
Explanation:
Since
(
x
n
)
′
=
n
·
x
n
−
1
,
holds for all integers
n
, we see that
f
′
(
x
) = 6
x
2
+ 14
x
−
3
.
Hence
f
′
(
−
1) =
−
8
.
004
10.0 points
Determine the derivative of
f
when
f
(
x
) =
√
5
x
−
1
√
5
x
.
1.
f
′
(
x
) =
1
2
parenleftbigg
5
x
−
1
x
√
5
x
parenrightbigg
2.
f
′
(
x
) =
1
2
parenleftbigg
5
x
+ 1
√
5
x
parenrightbigg
3.
f
′
(
x
) =
5
x
−
1
√
5
x
4.
f
′
(
x
) =
5
x
−
1
x
√
5
x
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rabbani (tar547) – Homework05 – Fouli – (58395)
2
5.
f
′
(
x
) =
1
2
parenleftbigg
5
x
+ 1
x
√
5
x
parenrightbigg
correct
6.
f
′
(
x
) =
5
x
+ 1
x
√
5
x
Explanation:
Since
d
dx
a x
r
=
r a x
r
−
1
for all exponents
r
negationslash
= 0 and constants
a
, we
see that
f
′
(
x
) =
1
2
radicalbigg
5
x
+
1
2
1
x
√
5
x
.
After simplification this becomes
f
′
(
x
) =
1
2
parenleftbigg
5
x
+ 1
x
√
5
x
parenrightbigg
.
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 Fall '08
 JOUVE
 Derivative, Product Rule, Quotient Rule, Cos, Rabbani

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