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AIEEE 2007 Solved Paper
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© examsnet.com
Question : 98
Total: 118
A value of
c
for which conclusion of Mean Value Theorem holds for the function
f
(
x
)
=
log
e
x
on the interval
[
1
,
3
]
is
log
3
e
log
e
3
2
log
3
e
1
2
log
3
e
Validate
Solution:
Using Lagrange's Mean Value Theorem
Let
f
(
x
)
be a function defined on
[
a
,
b
]
then,
f
′
(
c
)
=
f
(
b
)
−
f
(
a
)
b
−
a
.....(i)
c
∈
[
a
,
b
]
∴
Given
f
(
x
)
=
log
e
x
∴
f
′
(
x
)
=
1
x
∴
equation
(
i
)
become
1
c
=
f
(
3
)
−
f
(
1
)
3
−
1
⇒
1
c
=
log
e
3
−
log
e
1
2
=
log
e
3
2
⇒
c
=
2
log
e
3
⇒
c
=
2
log
3
e
© examsnet.com
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