WBJEE · Maths · Application of Derivatives
If \(f(x)=\sin x+2 \cos ^{2} x, \frac{\pi}{4} \leq x \leq \frac{3 \pi}{4} .\) Then, \(f\) attains its
- A minimum at \(x=\frac{\pi}{4}\)
- B maximum at \(x=\frac{\pi}{2}\)
- C minimum \(x=\frac{\pi}{2}\)
- D maximum at \(x=\sin ^{-1}\left(\frac{1}{4}\right)\)
Answer & Solution
Correct Answer
(C) minimum \(x=\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\sin x+2 \cos ^{2} x, x \in\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]\) \(\therefore \quad f^{\prime}(x)=\cos x-4 \cos x \cdot \sin x\) and \(f^{\prime}(x)=-\sin x-4 \cos 2 x\) For maximum or minimum of \(f(x)\) Put \(\quad f^{\prime}(x)=0\)…
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