Hey I need help with this question and any help will be appreciated. We have to use mathematica but I dont know how.
A polynomial pn(x) of degree n which agrees with a function f(x) at n+1 points x0,...,xn. Another type of polynomial interpolation finds a degree n polynomial Pn(x) so that n derivatives of P(x) agree with the corresponding derivatives of f(x) at xo or
P(xo) = f(xo), P`(xo) = f`(xo), ... , P^(n)(xo) = f^(n)(xo).
1. Find an explicit formula for Pn(x) in terms of xo and f(xo), f`(xo), ... , f^(n)(xo).
2. Give an error bound for the difference between Pn(x) and f(x) in terms of (x - xo)^(n+1).