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Test Index
JEE Main Math Class 12 Limits and Derivatives Part 1 Questions
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© examsnet.com
Question : 19
Total: 100
Let
f
:
R
→
R
satisfy
f
(
x
+
y
)
=
2
x
f
(
y
)
+
4
y
f
(
x
)
,
∀
x
,
y
∈
R
. If
f
(
2
)
=
3
, then
14
.
f
′
(
4
)
f
′
(
2
)
is equal to___
[26-Jun-2022-Shift-2]
Your Answer:
Validate
Solution:
👈: Video Solution
∵
f
(
x
+
y
)
=
2
x
f
(
y
)
+
4
y
f
(
x
)
.
.
.
.
.
.
(
1
)
Now,
f
(
y
+
x
)
2
y
f
(
x
)
+
4
x
f
(
y
)
.
.
.
.
.
.
(
2
)
∴
2
x
f
(
y
)
+
4
y
f
(
x
)
=
2
y
f
(
x
)
+
4
x
f
(
y
)
(
4
y
−
2
y
)
f
(
x
)
=
(
4
x
−
2
x
)
f
(
y
)
f
(
x
)
4
x
−
2
x
=
f
(
y
)
4
y
−
2
y
=
k
∴
f
(
x
)
=
k
(
4
x
−
2
x
)
∵
f
(
2
)
=
3
then
k
=
1
4
∴
f
(
x
)
=
4
x
−
2
x
4
∴
f
′
(
x
)
=
4
x
ln
4
−
2
x
ln
2
4
f
′
(
x
)
=
(
2.4
x
−
2
x
)
ln
2
4
∴
f
′
(
4
)
f
′
(
2
)
=
2.256
−
16
2.16
−
4
∴
14
f
′
(
4
)
f
′
(
2
)
=
248
© examsnet.com
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