Caught Similarities

Calculus Level 3

Let f(x)f(x) be a second degree polynomial such that

{f(0)+f(0)+f(0) ⁣ ⁣ ⁣ ⁣ ⁣=12f(1)+f(1)+f(1) ⁣ ⁣ ⁣ ⁣ ⁣=13f(2)+f(2)+f(2) ⁣ ⁣ ⁣ ⁣ ⁣=23 \left\{\begin{matrix} f(0)+f'(0)+f''(0) \! \! \! \! \! &=12\\ f(1)+f'(1)+f''(1) \! \! \! \! \! &=13\\ f(2)+f'(2)+f''(2) \! \! \! \! \! &=23 \end{matrix}\right.

Evaluate f(3)+f(3)+f(3)f(3) + f'(3) + f''(3).

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