Find the vales of ‘a’ for which the function f(x) = sinx – ax + 4 is increasing function on R.

f(x) = Sin x – ax + 4

f’(x) = Cos x – a + 0

f’(x) = Cos x – a

f(x) is increasing on R.

f’(x) > 0

Cos x – a > 0

Cos x > a

Cos x ≥ -1, ∀x ϵ R

a < -1

a ϵ (-∞, -1)

Hence the required set of values is a ϵ (-∞, -1).