If the function f(x) = cos |x| -2ax + b

CUET Preparation Today

Start Free Mocks

Home Questions Q9A7P85D5V

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

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

Options:

a ≤ b

$a=\frac{b}{2}$

$a≤-\frac{1}{2}$

$a≥-\frac{3}{2}$

Correct Answer:

$a≤-\frac{1}{2}$

Explanation:

Here $f'(x) ≥ 0, ∀x ∈ R$

$⇒ -sinx - 2a ≥ 0, ∀x ∈ R$

$⇒ a ≤ -\frac{sinx}{2} ⇒ a ≤ -\frac{1}{2}$.

Hence (C) is the correct answer.