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JEE Main Math Class 12 Application of Derivatives Part 3 Questions
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© examsnet.com
Question : 39
Total: 40
If the functions
f
(
x
)
=
x
3
3
+
2
b
bx
+
a
x
2
2
and
g
(
x
)
=
x
3
3
+
a
x
+
b
x
2
,
a
≠
2
b
have a common extreme point, then
a
+
2
b
+
7
is equal to
[30-Jan-2023 Shift 2]
4
3
2
3
6
Validate
Solution:
f
′
(
x
)
=
x
2
+
2
b
+
a
x
g
′
(
x
)
=
x
2
+
a
+
2
bx
(
2
b
−
a
)
−
x
(
2
b
−
a
)
=
0
∴
x
=
1
is the common root
Put
x
=
1
in
f
′
(
x
)
=
0
or
g
′
(
x
)
=
0
1
+
2
b
+
a
=
0
7
+
2
b
+
a
=
6
© examsnet.com
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