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MCQMediumJEE 2023Applications of Derivatives (Monotonicity, Extrema)

JEE Mathematics 2023 Question with Solution

Find the maximum value of the function

Expression asking for the maximum of a function over the interval from zero to pi, involving x, sine x cosine x, and sine 3x.
  • A

    00

  • B

    π\pi

  • C

    5π+2+336\frac{5\pi + 2 + 3\sqrt{3}}{6}

  • D

    π+2−336\frac{\pi + 2 - 3\sqrt{3}}{6}

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: Find the maximum value of the function shown in the image over 0≤x≤π0 \le x \le \pi.

Find: The maximum value of

f(x)=x−2sin⁡xcos⁡x+13sin⁡3xf(x)=x-2\sin x\cos x+\frac{1}{3}\sin 3x

the solution is unrelated to this question, so the answer is resolved from the given correct answer field. Therefore, the correct option is C, corresponding to

5π+2+336\frac{5\pi + 2 + 3\sqrt{3}}{6}

Common mistakes

  • Treating the provided RL-circuit solution as applicable here is incorrect because it is for a different question. Use only the question expression and the consistent answer source for this problem.

  • Ignoring the interval 0≤x≤π0 \le x \le \pi can lead to choosing a local extremum outside the allowed domain. Always check critical points and endpoints within the stated interval.

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