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KEAM 2013 Math Paper
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© examsnet.com
Question : 100
Total: 120
If the slope of
y
=
3
x
2
+
a
x
3
is maximum at
x
=
1
2
,
then the value of
a
is equal to
2
1
−
1
−
2
3
Validate
Solution:
Given curve is
y
=
3
x
2
+
a
x
3
On differentiating w.r.t.
x
, we get
d
y
d
x
=
6
x
+
3
a
x
2
=
m
(
say
)
....(i)
Now, differentiating Eq. (i) w.r.t.
x
, we get
d
m
d
x
=
6
+
6
a
x
and
d
2
m
d
x
2
=
6
a
For maximum or minimum of
m
,
put
d
m
d
x
=
0
⇒
6
+
6
a
x
=
0
⇒
x
=
−
1
a
<
0
0 (max)
But given
m
is maximum at
x
=
1
2
.
∴
−
1
a
=
1
2
⇒
a
=
−
2
© examsnet.com
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