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WBJEE 2018 Math Solved Paper
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© examsnet.com
Question : 69
Total: 75
Let f(x) =
c
o
s
(
π
x
)
, x ≠ 0 then assuming k as an integer
f(x) increases in the interval
(
1
2
k
+
1
,
1
2
k
)
f(x) decreases in the interval
(
1
2
k
+
1
,
1
2
k
)
f(x) decreases in the interval
(
1
2
k
+
2
,
1
2
k
+
1
)
f(x) increases in the interval
(
1
2
k
+
2
,
1
2
k
+
1
)
Validate
Solution:
f(x) =
c
o
s
(
π
x
)
f'(x) =
−
s
i
n
(
π
x
)
(
−
π
x
)
=
π
x
2
s
i
n
(
π
x
)
>
0
for increasing function f'(x) > 0
⇒
s
i
n
(
π
x
)
>
0
(
2
k
π
)
<
π
x
<
(
2
k
+
1
)
π
1
2
k
>
x
>
1
(
2
k
+
1
)
for decreasing function f'(x) < 0
s
i
n
(
π
x
)
<
0
π
x
∈
(
(
2
k
+
1
)
π
,
(
2
k
+
2
)
π
)
⇒
x
∈
(
1
2
k
+
2
,
1
2
k
+
1
)
© examsnet.com
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