Question: Do there exist a, b, c and d so that the function S(x) = ax^3 + x^2 + cx 1 < x < 0 bx^3

Do there exist a, b, c and d so that the function

S(x) = ax^3 + x^2 + cx 1 < x < 0

bx^3 + x^2 + dx 0 < x < 1 .

is a natural cubic spline?

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