Question

Find the values of ‘a’ for which the function f(x) = b – ax + sin x is increasing on R.

Answer 1

f(x) = b – ax + sin x

For f(x) to be increasing on R.

f'(x) = –a + cos x ≥ 0

⇒ cos x ≥ a

But for all real x,

 –1 ≤ cos x ≤ 1

So the inequality cos x ≥ a must hold even for the smallest value −1.

a ≤ –1