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JEE Main Math Class 12 Application of Derivatives Part 3 Questions
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© examsnet.com
Question : 2
Total: 40
Let
f
:
ℝ
⟶
ℝ
be a thrice differentiable function such that
f
(
0
)
=
0
,
f
(
1
)
=
1
,
f
(
2
)
=
−
1
,
f
(
3
)
=
2
and
f
(
4
)
=
−
2
. Then, the minimum number of zeros of
(
3
f
′
f
′
′
+
f
′
′
′
)
(
x
)
is .....
[4 Apr 2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
(
3
f
′
f
′
′
+
f
f
′
′
′
)
(
x
)
=
(
(
f
f
′
′
+
(
f
′
)
2
)
(
x
)
)
′
(
f
f
′
′
+
(
f
′
)
2
)
(
x
)
=
(
(
f
f
′
)
(
x
)
)
′
∴
(
3
f
′
f
′
′
+
f
′
′
′
)
(
x
)
=
(
f
(
x
)
⋅
f
′
(
x
)
)
′
′
min
. roots of
f
(
x
)
⟶
4
∴
min. roots of
f
′
(
x
)
⟶
3
∴
min
. roots of
(
f
(
x
)
⋅
f
′
(
x
)
)
⟶
7
∴
min
roots of
(
f
(
x
)
⋅
f
′
(
x
)
)
"
⟶
5
© examsnet.com
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