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Byju's Answer
Standard XII
Mathematics
Condition for Monotonically Decreasing Function
Function fx...
Question
Function
f
(
x
)
=
x
3
−
3
x
2
−
9
x
+
22
is monotonic decreasing for
A
−
1
<
x
<
3
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B
1
<
x
<
3
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C
−
3
<
x
<
1
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D
None of these
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Solution
The correct option is
A
−
1
<
x
<
3
f
(
x
)
=
x
3
−
3
x
2
−
9
x
+
22
Given
f
is monotonic decreasing, so
f
′
(
x
)
<
0
f
(
x
)
=
3
x
2
−
6
x
−
9
<
0
⇒
x
2
−
2
x
−
3
<
0
⇒
−
1
<
x
<
3
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0
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