Find ‘a’ for which f(x) = a (x + sinx) + a is increasing on R.

Question

Philoid · Accepted Answer

f(x) = a (x + Sin x) + a

f’(x) = a (1 + Cos x) + 0

f’(x) = a (1 + Cos x)

For f(x), to be increasing, it must have,

f’(x) > 0

a (1 + Cos x) > 0 -------------- (i)

-1 ≤ Cos x ≤ 1, ∀x ϵ R

0 ≤ (1 + Cos x) ≤ 2, ∀x ϵ R

a > 0 {From eq. (i)}

a ϵ (0, ∞)

Hence the required set of values is a ϵ (0, ∞).