JEE Mains · Maths · STD 12 - 6. Application of derivatives
\(\max _{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}=\)
- A \(\frac{5 \pi+2+3 \sqrt{3}}{6}\)
- B \(\frac{\pi+2-3 \sqrt{3}}{6}\)
- C \(\pi\)
- D \(0\)
Answer & Solution
Correct Answer
(A) \(\frac{5 \pi+2+3 \sqrt{3}}{6}\)
Step-by-step Solution
Detailed explanation
\(f(x)=x-\sin 2 x+\frac{1}{3} \sin 3 x\) \(f^{\prime}(x)=1-2 \cos 2 x+\cos 3 x=0\) \(x=\frac{5 \pi}{6}, \frac{\pi}{6}\) \(\therefore f^{\prime \prime}(x)=4 \sin 2 x-3 \sin 3 x\) \(f^{\prime \prime}\left(\frac{5 \pi}{6}\right) < 0\)…
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