question about interpolation polynomial.?

Question

what is the appropriate interpolation degree of f(x)=ln(x) ?
for x=2.35 to 2.39 with h=0.01

and how can i find the appropriate degree of interpolation ???

Answer 1

get the answer from below web

Answer 2

You have only 2 "known" points, so your degree is 1:
p(x) = 0.85441(x - 2.39)/(2.35 - 2.39) + 0.8713(x - 2.35)/(2.39 - 2.35)
p(x) = 0.8544(x - 2.39)/-0.04 + 0.8713(x - 2.35)/0.04
p(x) = -21.36(x - 2.39) + 21.7823(x - 2.35)
p(x) = -21.36x + 51.0513 + 21.7823x - 51.1888
p(x) = 0.4223x - 0.1375,
with an average error of 0.055%