The number of points in the interval `[-sqrt(13) sqrt(13)]` at which f(x)`=sin x^2 +cos x^2 ` attains its maximum value is

Options

A. 2
B. 8
C. 0
D. 4

Answer

D

Explanation

We have `f(x)=sin x^2 + cos x^2`
`f(X)=sqrt(2)(cos ""x^2 cos"" pi/4 + sin"" x^2 sin"" pi/4}=sqrt(2) cos (x^2 - pi/4)`
For f(x) to be maximum we must have `x^2-pi/4=2n pi , n in N`
`rArr x= pm sqrt(2n pi + pi/4)`
`rArr x= pm sqrt(pi/4),pm sqrt((9 pi )/4) "as x" in [-sqrt(13),sqrt(3)]`