Finite Differences

Relationship between the finite differences and the equation of the polynomial function:


Example: If the 5th difference is 24, and the leading coefficient is 4, then the relation would be used as follows:


24 = 4 × 5!


(note that the exclamation mark means factorial)



This formula can be used to find certain information .. I.e. if the data is given, and the finite difference is found, then it is possible to find the leading coefficient.


i.e. if the 3rd difference is 30 :


30 = a × 3!

30 = a × 6

30/6 = a

a = 5


Therefore it is found that the leading coefficient is 5.







Using a set of x and y values, subtract the first value from the second and keep doing that until the end of the data set, if the new row isn't constant, then do it again, and again until a constant value is found:




If you have any questions, leave them in the comments below.