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To determine the spacing \( h \) in a table of equally spaced values for the function \[ f(x) = (2 + x)^4, \quad 1 \leq x \leq 2, \] such that the quadratic interpolation satisfies \( | \text{error} | \leq 10^{-6} \), we use the error formula for quadratic interpolation: \[ E(x) = \frac{f'''(\xi)}{6} (x - x_0)(x - x_1)(x - x_2) \] where \( \xi \) is some point in the interval \( [x_0, x_2] \). The maximum error occurs at the midpoints of the __________ _______ __________ ______ ________ ___ _____.
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