# Don't Even Try Guessing

Algebra Level 2

Let $$f(x)=a_0+a_1x+........+a_{n-1}x^{n-1}+a_nx^n$$ be a polynomial with non-negative real coefficients, such that $$f(9)=3$$ and $$f(81)=27$$. Find the maximum possible achievable value of $$f(27)$$.

Extra Credit: Find all polynomials having the equality case.

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