Published by:
CGP EDU Academic Team
Published on: August 11, 2026
If the function ƒ(x) = 
sin (x – 2) + a cos (x – 2), (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then -
Text Solution
Verified by ExpertsThe correct answer is:
C
We have, x ∈ (4, 6)
⇒ 2 < x – 2 < 4
⇒ 
, a > 0
For ƒ(x) to be continuous and differentiable in (4, 6), 
must attain a constant value for x ∈ (4, 6)
Clearly, this is possible only when a ≥ 64
In that case, we have
ƒ(x) = a cos (x – 2) which is continuous and differentiable
∴ a ∈ [64, ∞ )
Hence, is the correct answer.
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