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Manipal Entrance Test 2015 Math Paper
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© examsnet.com
Question : 52
Total: 70
The greatest value of the function
f
(
x
)
=
x
e
−
x
in
[
0
,
∞
)
,
is
0
1
e
−
e
e
Validate
Solution:
We have,
f
(
x
)
=
x
e
−
x
On differentiating both sides w.r.t. x, we get
f
′
(
x
)
=
e
−
x
(
1
−
x
)
Put
f
′
(
x
)
=
0
⇒
x
=
1
Now, f(0) = 0
and
lim
x
→
∞
f
(
x
)
=
lim
x
→
∞
x
e
−
x
=
lim
x
→
∞
x
e
x
=
lim
x
→
∞
1
e
x
=
0
Hence, the greatest value of
f
(
x
)
is
1
e
.
© examsnet.com
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