Find the set of values of a’a’ for which f(x) = x + cosx + ax + b is increasing on R.

Question

Philoid · Accepted Answer

f(x) = x + Cos x + ax + b

f’(x) = 1 – Sin x + a + 0

f’(x) = 1 – Sin x + a

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

f’(x) > 0

1 – Sin x + a > 0

1 > Sin x - a

Sin x < a + 1

the maximum value of Sin x is 1.

Also, 1 < a + 1

a > 0

a ϵ (0, ∞)

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