There is a cubic polynomial \(f(x)\) with values of \(x\) lying in the interval \([-1,2]\). Given the following clues:

\(f'''(x)=24\)

An extreme of \(f'(x)\) lies at \(x=\frac{-1}{6}\)

The coefficients of \(x, x^{0}\) in \(f(x)\) are \(0,6\) respectively.

Find the maximum of \(f(x)\)

Try Part 1

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