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Test Index
JEE Main Math Class 12 Application of Derivatives Part 2 Questions
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© examsnet.com
Question : 20
Total: 100
Let
f
(
x
)
=
3
(
x
2
−
2
)
3
+
4
,
x
∈
R
. Then which of the following statements are true?
P
:
x
=
0
is a point of local minima of
f
Q
:
x
=
√
2
is a point of inflection of
f
R
:
f
′
is increasing for
x
>
√
2
[29-Jul-2022-Shift-1]
Only P and Q
Only P and R
Only Q and R
All P, Q and R
Validate
Solution:
f
(
x
)
=
3
(
x
2
−
2
)
3
+
4
,
x
∈
R
f
(
x
)
=
81.3
(
x
2
−
2
)
3
f
′
(
x
)
=
81.3
(
x
2
−
2
)
3
ln
2.3
(
x
2
−
2
)
2
x
=
(
486
ln
2
)
(
3
(
x
2
−
2
)
3
(
x
2
−
2
)
x
)
⇒
x
=
0
is the local minima.
f
′
′
(
x
)
=
(
486
ln
2
)
(
3
(
x
2
−
2
)
3
⋅
(
x
2
−
2
)
(
5
x
2
−
2
+
6
x
2
ln
3
(
x
2
−
2
)
)
)
f
′
′
(
x
)
=
0
x
=
√
2
f
′
′
(
√
2
+
)
>
0
f
′
′
(
√
2
−
)
<
0
⇒
x
=
√
2
is point of inflection
f
′
′
(
x
)
>
0
∀
x
>
√
2
⇒
f
′
(
x
)
is increasing for
x
>
√
2
© examsnet.com
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