CUET · MATHS · PYQ PAPER 2023
The value of b for which the function \(f(x) = \sin x - bx + C\), where b and C are constants is decreasing for \(x \in R\) is given by
- A \(b < 1\)
- B \(b \ge 0\)
- C \(b > 1\)
- D \(b \le 1\)
Answer & Solution
Correct Answer
(C) \(b > 1\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \cos x - b\) For \(f(x)\) to be decreasing, \(f'(x) \le 0\) for all \(x \in R\). \(\cos x - b \le 0 \implies \cos x \le b\) Since \(\max(\cos x) = 1\), for \(\cos x \le b\) to hold for all \(x\), we must have \(b \ge 1\). Considering the given options, the only option…
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