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Constructing a polynomial

(a) Consider the function values...
Consider a polynomial P(x) of least degree (the osculating polynomial) through the points xi=x0+i*h, i.e. polynomial that satisfies
P(x0)=f0, P(x1)=f1, P'(x1)=f'(x1), P(x2)=f2

(b) Prove that df(x1)/dx = dP(x1)/dx for any smooth function f(x)
(c) Construct the polynomial P(x) for the function f(x)=sin(x) and x0=0, x1=pi/2, x2=pi

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Solution Preview

please check the file Q38306 Polynomial.doc

UPDATE: Question from Student:
For the first part of the question, would the answer simply be all those equations? There is no one way of ...

Solution Summary

This shows how to construct a polynomial for a given situation.