Numerical Analysis Question?

[d_u_guy]

Use Newton forward difference formula to construct interpolating polynomials of degree one and degree two

a. f(0)=1, f(0.25)=1.64872,
f(0.5)=2.71828, f(0.75)=4.48169


b. Find P(0.23)


c. Use Newton backward diference formula to construct interpolating polynomials of degree one and degree two for the date in 2(a)


d. Evaluate P(0.43)

[roman_king1]

a)
Step 1: Construct the table:
h = 0.25
x --------- f(x) ------------ ∆f -----------∆^2f -------∆^3f
0 --------- 1
----------------------------- 0.64872
0.25------1.64872 ------------------- 0.42084
----------------------------- 1.06956 ---------------- 0.27301
0.5-------- 2.71828 ------------------ 0.69385
------------------------------ 1.76341
0.75------ 4.48169

Follow this instructions:
http://kr.cs.ait.ac.th/~radok/math/mat7/step22.htm