Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The values of 'a' for which the function
f(x) = sin 2x + 2x – ax + b is either always increasing or always decreasing for all x ∈ R, are :
Text Solution
Verified by ExpertsThe correct answer is:
C
f(x) = sin 2x + 2x – ax + b
f '(x) = 2cos 2x + 2 – a
Case-1 f( λ ) is always increasing
⇒ f '(x) > 0 
x ∈ R.
⇒ 4cos 2 x > 0 ⇒ a < 0 Min of cos 2 x = 0
Case-2 f(x) is always decreasing
f '(x) < 0 then
⇒ 4cos 2 x < a ⇒ a > 4 Max. of cos 2 x = 1
Hence a < 0 or a > 4
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