Question

Given these data:

x	1	2	3	5	7	8
f(x)	3	6	19	99	291	444

a) Calculate f(4) using Newton's interpolating polynomials of order 1 through 4. Choose your base points to attain good accuracy. What do your results indicate regarding the order of the polynomial used to generate the data in the table?

Answer 1

sorbet 7°17 given х 2 3 5 7 8 bi 6 99 291 444 f(x) 3 interpolating Newtons Polynomials. Ph(x) f (x) + f (te, ki :) (2 -20) + f(xoito, xord] (6-10) 6.- Ly) + f (Nox, Aq kg tx-ko) (x-2) (x -*2) +P [ro. Go, Yoga Muz Kon] (x - 1) (x-*,) (x-22) (x-hoz) +P [nom, le day xp ly) is des) (0-x) (6-4) (x-2-3) (x-x-2y) f [ho] f (as) of Cto) f [to, ry] 1 - 0 2-1

f[mo, xog] feuz) -f(x) 2 = 19-6 13 3-2 , , M, L, -7 -8 + ) Xq-ho 5 3- f [mg tog flog) .flue) Xz-x-2 99-19 2 40 9 - 3 F [2, X2, 63] f (wg ty) - f (x, xe) X3-1, 40-13 9 r [no to, da tez f (xos xq 23) - F bio.2, hogy henzho 9-5 5-1

FL- - - - - F (-, , 55) Е [+o , , +а и «Ort - R4 гръг, , , , ) F[la hy ko) p (r, de hy) to-v, гр. з .7 уру ч] - fL... . . "L,3 C+1 €1) а PLън) - F (23) Maghz , 991-qq - 46 1- - 1 4 +11 а ъ, 7 ЧЕ -40 3 nih гр., м.-э..] е 1 ч. 9 29 е } • О с Lз ә4 ch t-L Фо) all vales of fon (x) е, (x) 3+ 3 (ъ) +3 C -1) (ъ - 2) + 1 (x-1) X-2) Съ-3)

Pu (x=4) : 3+3 (4-1) +5(4-1) (4-2) +4-1)(4-2) (4-3) 3+ 9 + 6x51 t 3x2x1 3+9 +30 + 6 48 should only required for generate we the data up to 4 point means z