I have to approximate the second derivative of a function $f : \Bbb R \rightarrow \Bbb R$ at the point $x$. There we evaluate the function for a $h > 0$ at the points $t_0 = x-h $, $t_2 = x$ and $t_3 = x +h$. I have the interpolation polynomial $p$ of second degree by these points and evaluate $S = p''(x)$.
Basically I just have to proof that $$ S = \alpha f(x-h) + \beta f(x) + \gamma f (x+h) $$ holds with $\alpha, \beta, \gamma \in \Bbb R$. And also evaluate $\alpha, \beta, \gamma$.
How do I even start?