3. Consider interpolating a function f with a polynomial p Pn of the form n p(x)...

  

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3. Consider interpolating a function f with a polynomial p Pn of the form n p(x) = a(x xo), i=0 (1) where xo is given. We need n + 1 distinct interpolation conditions in order to compute p. Assuming fe Cn near xo, all of these conditions could be specified at xo as follows: pi) (ro) = f()(xo), i = 0...n. (2) Note this is an instance of the generalized interpolation problem discussed in lecture. Write out and solve the linear system corresponding to conditions (2) using form (1) of p. The resulting polynomial should look very familiar. What is it? 3. Consider interpolating a function f with a polynomial p Pn of the form n p(x) = a(x xo), i=0 (1) where xo is given. We need n + 1 distinct interpolation conditions in order to compute p. Assuming fe Cn near xo, all of these conditions could be specified at xo as follows: pi) (ro) = f()(xo), i = 0...n. (2) Note this is an instance of the generalized interpolation problem discussed in lecture. Write out and solve the linear system corresponding to conditions (2) using form (1) of p. The resulting polynomial should look very familiar. What is it?