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UPSEE 2018 Solved Paper
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© examsnet.com
Question : 126
Total: 150
If the function
f
(
x
)
=
a
log
|
x
|
+
b
x
2
+
x
has its extremum values at
x
=
−
1
and
x
=
2
, then the values of a and
b
.
a
=
2
b
=
1
2
a
=
1
2
,
b
=
2
a
=
2
,
b
=
−
1
2
a
=
−
2
,
b
=
−
1
2
Validate
Solution:
We have,
f
(
x
)
=
a
log
|
x
|
+
b
x
2
+
x
f
′
(
x
)
=
a
x
+
2
b
x
+
1
Since,
f
(
x
)
has extremum value at
x
=
−
1
and
x
=
2
∴
f
′
(
−
1
)
=
0
and
f
′
(
2
)
=
0
∴
f
′
(
−
1
)
=
−
a
−
2
b
+
1
=
0
......(i)
f
′
(
2
)
=
a
2
+
4
b
+
1
=
0
.......(i)
On solving Eqs. (i) and (ii), we get
a
=
2
,
b
=
−
1
2
© examsnet.com
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