WBJEE · Maths · Application of Derivatives
The value of \(K\) in order that \(f(x)=\sin x-\cos x-K x+5\) decreases for all positive real values of \(x\) is given by
- A \(K < 1\)
- B \(K \geq 1\)
- C \(K>\sqrt{2}\)
- D \(K < \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(K>\sqrt{2}\)
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} f(x) &=\sin x-\cos x-K x+5 \\ \Rightarrow f^{\prime}(x) &=\cos x+\sin x-K \end{aligned}\) For decreasing,…
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