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Question
Mathematics
If f(x) = (a2 -1/a2 +1) x3 -3x +5 is a decreasing function of x in R, then the set of possible values of a (independent of x) is
Q. If
f
(
x
)
=
a
2
+
1
a
2
−
1
x
3
−
3
x
+
5
is a decreasing function of
x
in
R
, then the set of possible values of a (independent of
x
) is
2684
194
BITSAT
BITSAT 2012
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A
(
1
,
∞
)
67%
B
(
−
∞
,
−
1
)
33%
C
[
−
1
,
1
]
0%
D
None of these
0%
Solution:
f
′
(
x
)
=
3
(
a
2
+
1
a
2
−
1
)
x
2
−
3
f
′
(
x
)
<
0
for all
x
if
a
2
−
1
≤
0
⇒
−
1
≤
a
≤
1