Let k and m be positive real numbers such that the function f ( x ) = { 3 x 2 + k x + 1 , 0 x 1 m x 2 + k 2 , x 1 is differentiable for all x 0 . Then 8 f ' ( 8 ) f ' ( 1 8 ) is equal to ______ . [2023]

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Q.
Let $k$ and $m$ be positive real numbers such that the function $f (x) =$ ${\begin{matrix} 3 x^{2} + k \sqrt{x + 1}, & 0 < x < 1 \\ m x^{2} + k^{2}, & x \geq 1 \end{matrix}$ is differentiable for all $x > 0$ . Then $\frac{8 f' (8)}{f' (\frac{1}{8})}$ is equal to ______ . [2023]

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