Question

If the function f (x) = cos |x| – 2ax + b increases for all x ∈ R, then

• A. a ≤ b
• B. a = $\frac{b}{2}$
• C. a ≤$- \frac{1}{2}$
• D. a ≥$- \frac{3}{2}$

Answer 1

Answer: (C)

a ≤$- \frac{1}{2}$

Answer 2

Here f′ (x) ≥ 0, ∀ x ∈ R

⇒ -sin x –2a ≥ 0

⇒ a ≤ $- \frac{\sin x}{2}$ ⇒ a ≤ $- \frac{1}{2}$