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Calculus Level 4

A cubic polynomial \(f(x)\) vanishes at \(x=2\) i.e \(f(2)=0\) and has a relative minimum/maximum at \(x=-1\) and \(x=1/3\) respectively. If

\[\int _{ -1 }^{ 1 }{ f(x)dx } = \frac { 14 }{ 3 }, \]

find \( \lfloor f(-3) \rfloor \) .

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