Question

The function f(x) = kx – sin x is strictly increasing for ______.

Options

• k > 1

• k < 1

• k > –1

• k < –1

Answer 1

The function f(x) = kx – sin x is strictly increasing for k > 1.

Explanation:

f (x) = kx − sin x is strictly increasing for all x ∈ R

f'(x) > 0 ∀ x ∈ R

λ (0) > 0

= k − cos x > 0

= k − cos 0 > 0

= k − 1 > 0 ⇒ k > 1