If `f(x) = |{:( cos (2x) ,, cos ( 2x ) ,, sin ( 2x) ), ( - cos x,, cosx ,, - sin x ), ( sinx,, sin x,, cos x ):}|`, then

Options

A. f'(x) =0 at exactly three points in `(-pi,pi)`
B. f(x) attains its maximum at x=0
C. f(x) attains its mionimum at x=0
D. f'(x) =0 at more than three points in `(-pi,pi)`

Answer

2,4

Explanation

`f(x)={:|(cos(2x),cos(2x),sin(2x).(-cosx,cosx, -sinx),(sinx ,sinx ,cosx)|:}`
Now f(X) = -2 sin 2x-4 sin4x=0
`rarr 2 sin 2x(1+4 cos 2x)=0`
`rarr sin 2x=0 or cos 2x=1/4`
for cos 2x=`-1/4` there are four solution
f(x)=0 has more than three solution