Let f:S→S where S=0,∞ be a twice differentiable function such that fx+1=xfx. If g:S→R be defined as gx=logefx, then the value of g''5-g''1 is equal to :

Question

Let $f : S \to S$ where $S = (0, \infty)$ be a twice differentiable function such that $f (x + 1) = x f (x)$ . If $g : S \to R$ be defined as $g (x) = \log_{e} f (x)$ , then the value of $|g^{''} (5) - g^{''} (1)|$ is equal to :

\frac{205}{144}

\frac{197}{144}

\frac{187}{144}

1

Solution

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