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Byju's Answer
Standard XII
Mathematics
Condition for Monotonically Decreasing Function
The function ...
Question
The function
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
1
monotonically decreases for
A
1
<
x
<
3
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B
x
<
3
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C
x
>
1
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D
x
>
3
or
x
<
1
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Solution
The correct option is
A
1
<
x
<
3
f
(
x
)
=
x
3
−
6
x
2
+
9
x
+
1
f
(
x
)
=
3
x
2
−
12
x
+
9
For monotonically decreases
f
(
x
)
<
0
3
x
2
−
12
x
+
9
<
0
x
2
−
4
x
+
3
<
0
(
x
−
3
)
(
x
−
1
)
<
0
[
x
ϵ
(
1
,
3
)
]
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Standard XII Mathematics
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