Question

Let f (x) = ∫|log₂(log₃(log₄(cost + a)))|dt for t∈[0, x] be increasing for all real values of x, find a.

Answer 1

We have

f'(x) = |log₂(log₃(log₄(cosx + a)))|

Since f(x) is increasing, so f(x) is defined for all x.

(log₃(log₄(cosx + a))) > 0

(log₄(cosx + a)) > 1

(cosx + a) > 4

a > 4 – cosx

a > 5 for all x in R