Math 6610 • Analysis of Numerical Methods I

{Interpolation}

\textbf{a)} State the theorem about the existence and uniqueness of
interpolating polynomial. Give a proof. (You can consider any proof of your
choice).

\textbf{b)} Let \(f(x)=x^3+2x^2+x+1\). Find the polynomial of degree 4 that
interpolates the values of \(f\) at \(x=-2,-1,0,1,2\).

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