Question

f(x) = sin x - kx is decreasing for all x ∉ R, when

A. k < 1

B. k ≤ 1

C. k > 1

D. k ≥ 1

Answer 1

Answer is : D. k ≥ 1

f(x) = sin x - kx

f’(x) = cos x – k

∴ f decreases, if f’(x) ≤ 0

⇒ cos x – k ≤ 0

⇒ cos x ≤ k

So, for decreasing k ≥ 1.