JEE Advanced 2008 Mathematics question

Let g(x) = log f(x) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, for N = 1, 2, 3, …,

g''(N + ) - g''() =

Answer: (A)

Solution

Taking logs, g(x + 1) = log x + g(x); differentiating twice: . Put and add: \frac$12) -

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Question ID VK-037613