Intervals, Equalities and Functions - Part 2

Algebra Level 5

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 \(x\) and \(x^{0}\) in \(f(x)\) are 0 and 6 respectively.

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

Try Part 1

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