AP EAMCET · Maths · Application of Derivatives
The value c of the Rolle's theorem for the function \(\mathrm{f}(\mathrm{x})=2 \sin \mathrm{x}+\sin 2 \mathrm{x}\) in the interval \([0, \pi]\) is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{6}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\( \mathrm{f}'(\mathrm{x}) = 2\cos \mathrm{x} + 2\cos 2\mathrm{x} \) \( 2\cos \mathrm{x} + 2\cos 2\mathrm{x} = 0 \) \( \cos \mathrm{x} + (2\cos^2 \mathrm{x} - 1) = 0 \) \( 2\cos^2 \mathrm{x} + \cos \mathrm{x} - 1 = 0 \) \( (2\cos \mathrm{x} - 1)(\cos \mathrm{x} + 1) = 0 \)…
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