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1/|x| outside an interval and ax^2 + b inside is differentiable everywhere: find a and b

The same question, asked 2 times: 2021 Paper 9*, 30 Jan 2024. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 9

    77
    If f(x)={1∣x∣,∣x∣≥1ax2+b,∣x∣<1f(x)=\begin{cases}\dfrac{1}{|x|}, & |x|\geq 1 \\ ax^{2}+b, & |x|<1\end{cases} is differentiable at every point of its domain, then the values of aa and bb are respectively:

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  2. Question 2

    30 Jan 2024

    89
    If the function f(x)={1∣x∣,∣x∣≥2ax2+2b,∣x∣<2f(x) =\left\{ \begin{matrix} \frac{1}{|x|} & ,|x| \geq 2 \\ ax^{2}+ 2b, & |x| < 2 \end{matrix} \right. is differentiable on RR, then 48(a+b)48(a + b) is equal to