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troyer (lmt836) – Section 3.3 – isaacson – (55826)
1
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beFore answering.
001
10.0 points
±ind the value oF
f
′
(
a
) when
f
(
t
) =
2
t
+ 3
t
+ 5
.
1.
f
′
(
a
) =

8
a
+ 5
2.
f
′
(
a
) =

7
(
a
+ 5)
2
3.
f
′
(
a
) =

8
(
a
+ 5)
2
4.
f
′
(
a
) =
7
a
+ 5
5.
f
′
(
a
) =
7
(
a
+ 5)
2
correct
6.
f
′
(
a
) =
8
(
a
+ 5)
2
Explanation:
By defnition,
f
′
(
a
) = lim
h
→
0
f
(
a
+
h
)

f
(
a
)
h
.
Now, For the given
f
,
f
(
a
+
h
) =
2(
a
+
h
) + 3
a
+
h
+ 5
,
while
f
(
a
) =
2
a
+ 3
a
+ 5
.
Thus
f
(
a
+
h
)

f
(
a
) =
2(
a
+
h
) + 3
a
+
h
+ 5

2
a
+ 3
a
+ 5
=
p
(2(
a
+
h
) + 3)(
a
+ 5)

(
a
+
h
+ 5)(2
a
+ 3)
P
(
a
+
h
+ 5)(
a
+ 5)
.
But
{
2(
a
+
h
) + 3
}
(
a
+ 5)
= 2
h
(
a
+ 5) + (2
a
+ 3)(
a
+ 5)
,
and
(
a
+
h
+5)(2
a
+3) =
h
(2
a
+3)+(
a
+5)(2
a
+3)
.
Consequently,
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 Spring '11
 Cathy

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