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Byju's Answer
Standard IX
Mathematics
Product Law
The interval ...
Question
The interval in which the function
x
2
x
2
+
3
is concave up
A
(
1
,
∞
)
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B
(
−
∞
,
−
1
)
∪
(
1
,
∞
)
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C
(
0
,
∞
)
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D
(
−
1
,
1
)
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Solution
The correct option is
D
(
−
1
,
1
)
Given,
f
(
x
)
=
x
2
x
2
+
3
,
x
∈
R
⇒
f
′
(
x
)
=
6
x
(
x
2
+
3
)
2
⇒
f
′′
(
x
)
=
18
(
x
2
+
3
)
(
1
−
x
2
)
(
x
2
+
3
)
4
For concave up,
f
′′
(
x
)
>
0
⇒
1
−
x
2
>
0
⇒
x
2
−
1
<
0
⇒
x
∈
(
−
1
,
1
)
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1
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