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The question is:

Given the set of points,

(2, -8) (4, -240) (6, -1272) (7,-2373) (8, -4046) (10, -9960) (12, -20688)

determine the degree of the equation.

However I am given values at 2, 4, 6 etc so the method of finite differences cant' be used so have just concentrated on the three points at 6,7,8 but can't find.

Jean Marie
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Voltar
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  • Have you tried using finite differences on x = 2, 4, 6, 8, 10, 12? – Cyclicduck Sep 30 '17 at 20:05
  • Yes I have and it doesn't work out to a constant difference - however to use the method of finite differences the x has to be consecutive so can't use x-2,4,6,8,10,12 - the clue is in the 6,7,8 but it is eluding me right now – Voltar Sep 30 '17 at 20:38
  • That's not true - x doesn't need to be "consecutive". Think about it - if P is a polynomial over the reals, why should a spacing of "1" be special in any way? – Cyclicduck Oct 01 '17 at 01:12
  • the method of finite differences and the difference table states that it is n then (n+1), (n+2) .... – Voltar Oct 01 '17 at 17:14
  • Do you have any idea why it works? If you understand why it is true it should be clear that it works the same way for n+k, n+2k, etc. – Cyclicduck Oct 01 '17 at 18:40
  • Furthermore, it's also true that for any k points, I can find a degree n polynomial going through all of them if for any sufficiently large n, so there is no unique answer. Are you looking for the minimum possible degree? – Cyclicduck Oct 01 '17 at 18:57
  • If so, you know by finite differences on 2, 4, 6... that it's greater than 4, and since there are 7 points that it's at most 6. – Cyclicduck Oct 01 '17 at 19:04
  • ahhh, I think it is in that it is greater than 4 but at most six – Voltar Oct 01 '17 at 20:02

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