Exercises
[1F7]Difficulty:* . Given \(x_ 0{\lt}x_ 1{\lt}x_ 2{\lt}\ldots {\lt}x_ n\) and given real numbers \(a_{i,h}\) (with \(i,h=0,\ldots n\)) show that there is a polynomial \(p(x)\) such that \(p^{(i)}(x_ h)=a_{i,h}\).
This result is the starting point of the Hermit method of polynomial interpolation, see [ 49 ] .
Solution 1