Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
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
α
≠
β
\alpha\ne\beta
α
=
β
and
f
(
α
+
β
2
)
<
f
(
α
)
+
f
(
β
)
2
f\left(\frac{\alpha+\beta}{2}\right)<\frac{f(\alpha)+f(\beta)}{2}
f
(
2
α
+
β
)
<
2
f
(
α
)
+
f
(
β
)
for all
α
\alpha
α
and
β
\beta
β
, then smallest positive integral value of
λ
\lambda
λ
is (a) 1 (b) 2 (c) 3 (d) 4 (a) 1 (b) 2 (c) 3 (d) 4
Browse the problem library