0 ∴ Function is minimum at x=e. Hence, minimum value of f(x) at x=e is f(e)=e" >
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Manipal Entrance Test 2014 Math Paper
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© examsnet.com
Question : 78
Total: 80
The minimum value of
x
log
x
is
e
1
e
e
2
e
3
Validate
Solution:
Let
f
(
x
)
=
x
log
x
f
′
(
x
)
=
log
x
−
1
(
log
x
)
2
Pur
f
′
(
x
)
=
0
,
for maxima or minima, we get
log
x
−
1
=
0
⇒
x
=
e
Now,
f
"
(
x
)
=
(
log
x
)
2
.
1
x
−
(
log
x
−
1
)
.
2
log
x
x
(
log
x
)
4
⇒
f
"
(
e
)
=
1
e
−
0
1
=
1
e
>
0
∴ Function is minimum at
x
=
e
.
Hence, minimum value of
f
(
x
)
at
x
=
e
is
f
(
e
)
=
e
© examsnet.com
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