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Byju's Answer
Standard XII
Mathematics
Normal
Let a curve y...
Question
Let a curve
y
=
f
(
x
)
pass through the point
(
2
,
(
log
e
2
)
2
)
and have slope
2
y
x
log
e
x
for all positive real value of
x
.
Then the value of
f
(
e
)
is equal to
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Solution
Given:
d
y
d
x
=
2
y
x
log
e
x
⇒
d
y
y
=
2
d
x
x
ln
x
⇒
ln
(
y
)
=
2
ln
(
ln
x
)
+
C
∵
(
2
,
(
ln
2
)
2
)
lies on the curve
∴
ln
(
ln
2
)
2
=
2
ln
(
ln
2
)
+
C
⇒
C
=
0
∴
ln
(
y
)
=
2
ln
(
ln
x
)
⇒
y
=
(
ln
x
)
2
Now, at
x
=
e
y
=
(
ln
e
)
2
∴
y
=
1
=
f
(
e
)
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4
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Standard XII Mathematics
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