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Differentiation question

2025 · 2 Apr · Shift 1 · Q40

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JEE Main
Mathematics
Differentiation
2025 · 2 Apr · Shift 1 · Q40

Differentiation question

2025 · 2 Apr · Shift 1 · Q40

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

f: \mathbf{R} \rightarrow \mathbf{R}

be a twice differentiable function such that

(\sin x \cos y)(f(2 x+2 y)-f(2 x-2 y))=(\cos x \sin y)(f(2 x+2 y)+f(2 x-2 y))

, for all

x, y \in \mathbf{R}

. If

f^{\prime}(0)=\frac{1}{2}

, then the value of

24 f^{\prime \prime}\left(\frac{5 \pi}{3}\right)

is :

A
2
B
3
C
$-$ 3
D
$-$ 2

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