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Byju's Answer
Standard XII
Mathematics
Test for Monotonicity about a Point
The maximum v...
Question
The maximum value of the function
f
(
x
)
=
l
n
(
1
+
x
)
−
x
(where
x
>
−
1
) occurs at
x
=
0
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Solution
The correct option is
A
0
f
(
x
)
=
l
n
(
1
+
x
)
−
x
,
x
>
−
1
f
′
(
x
)
=
1
1
+
x
−
1
=
−
x
1
+
x
f
′
(
x
)
=
0
⇒
−
x
1
+
x
=
0
x
=
0
f
′′
(
x
)
=
−
[
(
1
+
x
)
(
1
)
−
x
(
1
)
(
1
+
x
)
2
]
f
′′
(
0
)
=
−
1
<
0
⇒
f
(
x
)
has maxima at
x
=
0
Suggest Corrections
0
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Test for Monotonicity about a Point
Standard XII Mathematics
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