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KEAM 2014 Math Paper
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© examsnet.com
Question : 33
Total: 120
The function
f
(
x
)
=
2
x
3
−
15
x
2
+
36
x
+
6
is strictly decreasing in the interval
(
2
,
3
)
(
−
∞
,
2
)
(
3
,
4
)
(
−
∞
,
3
)
∪
(
4
,
∞
)
(
−
∞
,
2
)
∪
(
3
,
∞
)
Validate
Solution:
Given,
f
(
x
)
=
2
x
3
−
15
x
2
+
36
x
+
6
On differentiating both sides w.r.t.
x
, we get
f
′
(
x
)
=
6
x
2
−
30
x
+
36
For strictly decreasing.
f
′
(
x
)
<
0
⇒
6
(
x
2
−
5
x
+
6
)
<
0
⇒
(
x
−
3
)
(
x
−
2
)
<
0
⇒
2
<
x
<
3
∴
x
∈
(
2
,
3
)
© examsnet.com
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