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Question
Mathematics
The value of x for which f(x) = x3 - 6x2 - 36x + 7 is increasing, belong to
Q. The value of
x
for which
f
(
x
)
=
x
3
−
6
x
2
−
36
x
+
7
is increasing, belong to
1970
204
COMEDK
COMEDK 2008
Application of Derivatives
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A
(
−
1
,
0
)
∪
(
1
,
5
)
4
17%
B
(
−
2
,
0
)
∪
(
1
,
6
)
37%
C
(
∞
,
2
)
∪
(
6
,
∞
)
28%
D
(
−
2
,
6
)
19%
Solution:
f
(
x
)
=
x
3
−
6
x
2
−
36
x
+
7
f
′
(
x
)
=
3
x
2
−
12
x
−
36
Now,
f
′
(
x
)
=
0
⇒
3
x
2
−
12
x
−
36
=
0
⇒
x
=
−
2
,
6
Hence,f(x) is increasing in
(
∞2
)
∪
(
6
,
∞
)