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Mathematics
Problem
Passage - 3 (Questions 67 to 69) Consider,
f
(
x
)
=
cos
2
x
+
2
x
λ
2
+
(
2
λ
+
1
)
(
λ
−
1
)
x
2
f(x)=\cos 2x+2x\lambda^2+(2\lambda+1)(\lambda-1)x^2
f
(
x
)
=
cos
2
x
+
2
x
λ
2
+
(
2
λ
+
1
)
(
λ
−
1
)
x
2
,
λ
∈
R
\lambda\in R
λ
∈
R
. If
f
(
x
)
f(x)
f
(
x
)
is increasing for all
x
∈
R
x\in R
x
∈
R
then number of values of
λ
\lambda
λ
is (a) 1 (b) 2 (c) 3 (d) infinite
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