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Calculus Level 4

A monic polynomial function \(p(x) \) of degree 5 increases in the interval \(x<1\) and \(x>3\) and decreases in the interval \(1<x<3\). Call \(f(x) \) the polynomial obtained by differentiating \(p(x) \) once with respect to \(x\).

Given that \(p(0) = 4\) and \(f(2) = 0 \). Calculate the value of \(f(4) \).

If you think that the data is insufficient, then submit 1 as your answer.

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