Properties of periodic functions and Leibnitz ruleHard

Twice Differentiable Function Integral Relation

Let f : (0,∞) → R be a twice differentiable function. If for some a ≠ 0, $\int\limits_0^1 {f\left( {\lambda x} \right)} \,d\lambda$ = af(x), f(1) = 1 and f(16) = $\frac{1}{8}$ , then 16 – $f'\left( {\frac{1}{{16}}} \right)$ is equal to ______,

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