MCQMediumJEE Main 2025 · 2 April, Shift 1Derivatives of Functions

Mathematics Question from JEE Main 2025 · 2 April, Shift 1

Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a twice differentiable function such that

(sin⁡xcos⁡y)(f(2x+2y)−f(2x−2y))=(cos⁡xsin⁡y)(f(2x+2y)+f(2x−2y))(\sin x \cos y)\big(f(2x + 2y) - f(2x - 2y)\big) = (\cos x \sin y)\big(f(2x + 2y) + f(2x - 2y)\big)

for all x,y∈Rx, y \in \mathbb{R}. If f′(0)=12f'(0) = \frac{1}{2}, then the value of 24f′′(5π3)24 f''\left(\frac{5\pi}{3}\right) is:

  • A

    22

  • B

    −3-3

  • C

    −2-2

  • D

    33

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