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MHT CET 2017 Math Solved Paper
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© examsnet.com
Question : 4
Total: 50
The maximum value of
f(x) =
log
x
x
(x ≠ 0, x ≠ 1) is
e
1
e
e
2
1
e
2
Validate
Solution:
(b) since,
f
(
x
)
=
log
x
x
After differentiating on both sides w.r.t. x, we get
f
′
(
x
)
=
x
⋅
1
x
−
log
x
⋅
1
x
2
=
1
−
log
x
x
2
For maximum or minimum value of f(x), put
f
′
(
x
)
=
0
⇒
1
−
log
x
x
2
=
0
⇒
logx
=
1
⇒
x
=
e
Now,
f
′
′
(
x
)
=
3
+
2
log
x
x
3
∴
f
′
′
(
e
)
=
−
1
e
3
<
0
After substituting x = e in eq. (i), we get
f
(
e
)
=
log
e
e
=
1
e
Hence, maximum value of
f
(
x
)
is
1
e
at x = e
© examsnet.com
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