Caught Similarities

Calculus Level 3

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

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

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

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