Interpolation using divided differences

[ACLerok]

Homework Statement

Given a set of data points, derive the interpolation polynomial using divided differences.

Homework Equations

The Attempt at a Solution

My main question is: How am I supposed to do this if they don't give f(x)? Can I just look at the plotted data points and 'guess' the function (cos,sin,tan) that will best fit them? As a test, I tried using f(x)=cosx and graphed the resulting equation but it did not meet at the given points.

 

[HallsofIvy]

One of us is very confused on this! The problem says "using divided differences". Are you saying you do not know what that is?

 

[ACLerok]

I know what it is. I'm saying that I am supposed to find the interpolation formula but they don't say what f(x). You need f(x) to calculate the divided differences.

 

[fluidistic]

No, you don't need to know f(x) but P(x) which is the interpolant polynome. They don't give f(x) but they give the value of f(x) at known points. From this, you can do the divided differences and build the P(x). All this without knowing f(x).