Storming Polynomial!

Calculus Level 4

If \(f(x)\) is a polynomial of degree 6 with leading coefficient \(2009\). And that \(f(1)=1 \), \(f(2)=3\), \(f(3)=5\), \(f(4) =7\), \(f(5)=9\) and \(f'(2)=2\). Find the sum of all the digits of \(f(6)\).

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