Question
Question: If f(x) = cosx + a<sup>2</sup>x + b is an increasing function for all values of x, then...
If f(x) = cosx + a2x + b is an increasing function for all values of x, then
A
a ∈ [-1, 1]
B
a ∈ (-∞,-1] ∪ [1, ∞)
C
a ∈ [-1, ∞)
D
a ∈ (-∞, 1]
Answer
a ∈ (-∞,-1] ∪ [1, ∞)
Explanation
Solution
f '(x) = −sinx + a2 ⇒ a2 ≥ sin x ∀ x ∈ R ⇒ a2 > 1
⇒ a ∈ (-∞, -1] ∪ [1, ∞)