Write the set of values of a for which f(x) = cosx + a2x + b is strictly increasing on R.
f(x) = Cos x + a2x + b
f’(x) = -Sin x + a2 + 0
f’(x) = a2 - Sin x
f(x) is strictly increasing on R
f’(x) > 0, ∀x ϵ R
a2 – Sin x > 0, ∀x ϵ R
a2 > Sin x, ∀x ϵ R
Maximum value of Sin x is 1.
a2 > Sin x, a2 is always greater than 1.
a2 > 1
a2 – 1 > 0
(a + 1) (a – 1) > 0
a ϵ (-∞, -1) ∪ (1, ∞)