Show that f [x0, x1,... , xn , x] = f (n+1) ((x)) (n + 1)! , for some (x). [Hint: From
Chapter 3, Problem 3.2.20(choose chapter or problem)
Show that f [x0, x1,... , xn , x] = f (n+1) ((x)) (n + 1)! , for some (x). [Hint: From Eq. (3.3), f (x) = Pn (x) + f (n+1) ((x)) (n + 1)! (x x0)(x xn ). Considering the interpolation polynomial of degree n + 1 on x0, x1,... , xn , x, we have f (x) = Pn+1(x) = Pn (x) + f [x0, x1,... , xn , x](x x0)(x xn ).]
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