# 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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