- For a function f and distinct points $\alpha$, $\beta$, $\gamma$; what is meant by $f[\alpha,\beta,\gamma]$?
- Find the Lagrange form for the polynomial $P(x)$ that interpolates $f(x) = \frac{4x}{x+1}$ at $0$, $1$ and $3$.
For (1), I can say that we have a difference divided:$ \frac{f[\gamma]-f[\beta]}{\gamma - \beta}$ but a little lost on handling for three.
For (2): $(x-0) \times f(1) \times f(3) + (x-1) \times f(0) \times f(3) + (x-3) \times f(0) \times f(1)$ Will this work?