The values of b for which the function $

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The values of b for which the function $f(x)=cos\, x +bx + a $ decreases on R are

Options:

[-1, 1]

(-∞, 1]

(-∞, -1]

(-1, 1)

Correct Answer:

(-∞, 1]

Explanation:

The correct answer is Option (2) → (-∞, 1]

$f(x)=\cos x +bx + a$

$f'(x)=-\sin x+b<0$

⇒ for $b∈(-∞,1]$

$-\sin x+b<0$

$f(x)$ → decreasing