Nevilles Method for approximation

[emptymaximum]

basically, i don't get it at all.
i understand that

x0 P0
P01
x1 P1 P012
P12
x2 P2

let's approximate f(x) where x is some number.

i have some Pi given and a Pi(i+1) and Pi(i+1)(i+2)
i also have the xi
i don't know what f(x) is, some unknown function.
how do i find the Pi(i+1)(i+2)?

one question i have is to fill the table.
i have another question where I'm supposed to approximate
$\sqrt{3}$ by using $f(x) = 3^x$ and i have values for x0 through x4, so being able to build that table and i'll be able to do that no problem right?

what i have done so far:
nothing, i don't know how to build the table. alls i want help with is table building please.

 

[emptymaximum]

UPDATE:

i figured out how to make the table by interpolating tables given.
thanks anyways.