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KEAM 2015 Math Paper
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© examsnet.com
Question : 3
Total: 120
The function
f
(
x
)
=
s
i
n
x
−
k
x
−
c
, where k and c are constants, decreases always when
k > 1
k ≥ 1
k < 1
k ≤ 1
k < -1
Validate
Solution:
f
(
x
)
=
sin
x
−
k
x
−
c
⇒
f
′
(
x
)
=
cos
x
−
k
∴
f
decreases, if
f
′
(
x
)
≤
0
⇒
cos
x
−
k
≤
0
⇒
cos
x
≤
k
So, for decreasing
k
≥
1
© examsnet.com
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