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JEE Main Math Class 12 Application of Derivatives Part 2 Questions
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© examsnet.com
Question : 4
Total: 100
Let
f
:
ℝ
→
ℝ
be a differentiable function such that
f
′
(
x
)
+
f
(
x
)
=
2
∫
0
f
(
t
)
dt
. If
f
(
0
)
=
e
−
2
, then
2
f
(
0
)
−
f
(
2
)
is equal to _______.
[1-Feb-2023 Shift 1]
Your Answer:
Validate
Solution:
d
y
d
x
+
y
=
k
y
⋅
e
x
=
k
⋅
e
x
+
c
f
(
0
)
=
e
−
2
⇒
c
=
e
−
2
−
k
∴
y
=
k
+
(
e
−
2
−
k
)
e
−
x
⇒
k
=
e
−
2
−
1
∴
y
=
(
e
−
2
−
1
)
+
e
−
x
f
(
2
)
=
2
e
−
2
−
1
,
f
(
0
)
=
e
−
2
2
f
(
0
)
−
f
(
2
)
=
1
© examsnet.com
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