# Math Help - Finite Difference of Polynomial Functions..

1. ## Finite Difference of Polynomial Functions..

My book is talking about 1st, 2nd and 3rd difference of a function with nowhere an explanation what it means. I've tried to Google it, but nothing relevant comes up.

It's asking me to find the 3rd difference for equation: $f(x)=2x^3-6x+5$

Then the next pages shows a table, with values between -3 and 3 for x, and values for f(x). The next column is 1st differences, then 2nd differences, and finally 3rd differences.
It looks like you just subtract the values from one column to get the result for the next column?

Then it is expecting me to know what the 3rd difference result should be by looking at the equation..Huh?

2. Originally Posted by NotSoBasic
My book is talking about 1st, 2nd and 3rd difference of a function with nowhere an explanation what it means. I've tried to Google it, but nothing relevant comes up.

It's asking me to find the 3rd difference for equation: $f(x)=2x^3-6x+5$

Then the next pages shows a table, with values between -3 and 3 for x, and values for f(x). The next column is 1st differences, then 2nd differences, and finally 3rd differences.
It looks like you just subtract the values from one column to get the result for the next column?

Then it is expecting me to know what the 3rd difference result should be by looking at the equation..Huh?
see what Dr. Math says about finite differences ...

Math Forum - Ask Dr. Math

3. Originally Posted by skeeter
see what Dr. Math says about finite differences ...

Math Forum - Ask Dr. Math
OK, so it appears that I was correct about it just being a matter of subtracting the terms to get the result for the next difference.
So now I've found that the 3rd difference is 12 (constant). What does that mean?

4. Originally Posted by NotSoBasic
OK, so it appears that I was correct about it just being a matter of subtracting the terms to get the result for the next difference.
So now I've found that the 3rd difference is 12 (constant). What does that mean?
when the third set of differences is a constant, it tells you that the function values can be modeled by a cubic (3rd degree) polynomial.

5. Originally Posted by skeeter
when the third set of differences is a constant, it tells you that the function values can be modeled by a cubic (3rd degree) polynomial.
That we would know from looking at the leading coefficient's degree?

6. Originally Posted by NotSoBasic
That we would know from looking at the leading coefficient's degree?
yes, but the idea is that you only have the function values and are working backwards ... you do not start with the polynomial in front of you.

7. Interesting, thank you.