Published by:
CGP EDU Academic Team
Published on: August 11, 2026
If f(x) = 
, then
A
f (x) attains its minimum at x = 0
B
f (x) attains its maximum at x = 0
C
= 0 at more than three points in (– π , π )
D
= 0 at exactly three points in (– π , π )
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(b,c)
Sol. f(x) = 
= cos2x – cos2x (–cos 2 x + sin 2 x) + sin2x (–2sinxcosx)
f(x) = cos4x + cos2x
∴ f(x) = 2cos 2 2x + cos2x –1
Let cos2x = t
⇒ f(x) = 2t 2 + t –1 and t ∈ [–1, 1]
f(x) attains its minima at t = 
∈ [–1, 1]
∴ 
= 
∴ 
= 2 + 1 –1 = 2……..(when cos2x = 1)
f ' (x) = –4sin4x –2sin2x
f ' (x) = 0 ⇒ 4sin4x + 2sin2x = 0
⇒ 8sin2xcos2x + 2sin2x = 0
⇒ 2sin2x(4cos2x+1) = 0 ⇒ sin2x = 0 or cos2x = 
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