Extended Divided Difference

Apr 2009
I have a question I need help on:
Approximate the function using a polynomial on the interval [-2,2] using only the values of:
\(\displaystyle f(x) = 2sin(\frac{1}{4}\pi x)\)
\(\displaystyle f'(x) = \frac{1}{2}\pi cos(\frac{1}{4}\pi x)\)
at the endpoints \(\displaystyle x = \frac{+}{}2\)

I understand the divided difference table, but I don't know how to construct it from a function and its derivative other than substituting values into f(x) given the interval and using those as the initial points to start the table off..but then I don't see where the derivative comes into it?

Any help is appreciated.

PS I couldn't work out how to do the plus-minus sign in LaTeX so what you're actually seeing is \frac{+}{} which doesn't really come out too well. It's meant to read 'at the endpoints x = +2