Consider , . If and for all and , then smallest positive integral value of…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider

f(x)=\cos 2x+2x\lambda^2+(2\lambda+1)(\lambda-1)x^2

\lambda\in R

. If

\alpha\ne\beta

and

f\left(\frac{\alpha+\beta}{2}\right)<\frac{f(\alpha)+f(\beta)}{2}

for all

\alpha

and

\beta

, then smallest positive integral value of

\lambda

is (a) 1 (b) 2 (c) 3 (d) 4