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JEE Advanced 2020 Full Test 7 Paper 2
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© examsnet.com
Question : 52
Total: 54
If the function
f
(
x
)
=
2
x
3
−
9
a
x
2
+
12
a
2
x
+
1
has a local maximum at
x
=
x
1
and a local minimum at
x
=
x
2
such that
x
2
=
x
1
2
,
then
a
is equal to _______
Your Answer:
Validate
Solution:
f
′
′
(
x
)
=
6
x
2
−
18
a
x
+
12
a
2
=
0
⇒
x
=
a
,
2
a
Given
x
2
=
x
1
2
,
so a cannot be negative. If
a
>
0
then local minimum occurs at
x
and local maximum at
x
=
a
.
Thus
x
1
=
a
and
x
2
=
2
a
⇒
2
a
=
a
2
⇒
a
=
2
(
if
a
=
0
,
f
(
x
)
is always increasing
)
© examsnet.com
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