Verified Solution • 2025–26 Session moderate

QJEEAdv17Mae976: JEE Advanced 2017 Mathematics - Class 12 JEEAdv17Mae976 Solution: If f ( x ) =

If f(x)=|cos⁡2xcos⁡2xsin⁡2x−cos⁡xcos⁡x−sin⁡xsin⁡xsin⁡xcos⁡x|,

then

Multiple Choice Options

  • A f(x) attains its minimum at x = 0
  • B f(x) attains its maximum at x = 0
  • C f'(x) = 0 at more than three points in ( −- π\pi , π\pi )
  • D f'(x) = 0 at exactly three points in ( −- π\pi , π\pi )

Step-by-Step Verified Solution

f(x)=|cos⁡2xcos⁡2xsin⁡2x−cos⁡xcos⁡x−sin⁡xsin⁡xsin⁡xcos⁡x|

cos⁡2x(cos⁡2x+sin⁡2x)−cos⁡2x(−cos⁡2x+sin⁡2x)+sin⁡2x(−sin⁡2x)\cos 2x({\cos ^2}x + {\sin ^2}x) - \cos 2x( - {\cos ^2}x + {\sin ^2}x) + \sin 2x( - \sin 2x)

=cos⁡2x+cos⁡4x= \cos 2x + \cos 4x

f′(x)=−2sin⁡2x−4sin⁡4xf'(x) = - 2\sin 2x - 4\sin 4x

=−2sin⁡2x(1+4cos⁡2x)= - 2\sin 2x(1 + 4\cos 2x)

At x = 0

f'(x) = 0 and f(x) = 2

Also, f'(x) = 0 sin2x = 0 or cos⁡2x=−14\cos 2x = {{ - 1} \over 4}

⇒x=nπ2\Rightarrow x = {{n\pi } \over 2} or cos⁡2x=−14\cos 2x = - {1 \over 4}

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