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JEE Advanced Mathematics question

MathematicsMethods of DifferentiationsJEE Advanced

Let , where is twice differentiable positive function on such that . Then for

g''(N + Missing argument for \frac\frac12) - g''(Missing argument for \frac\frac12) =

Answer: (A)

Solution

, so . Differentiating twice:

g''(x+1) - g''(x) = -.

Put and add (the left side telescopes):

g''(N + Missing argument for \tfrac\tfrac12) -

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Question ID VK-110667