The values of a for which the function f(x) = sin x − ax + b is increasing on R are:

The values of a for which the function f(x) = sin x − ax + b is increasing on R are:

• A. a ≤ −1
• B. a ≥ 1
• C. a < 1
• D. a > 1

Answer: A) a ≤ −1

Explanation: f'(x) = cos x − a. For f to be increasing, f'(x) ≥ 0 for all x → cos x ≥ a. Since max cos x = 1, min cos x = −1, we need a ≤ −1 so that cos x ≥ a always holds.