Solve Finite Difference: Find Constant Equation

AI Thread Summary
The discussion revolves around solving a finite difference problem to find a constant equation, specifically using the example y=10x^4, where the constant is identified as 240. Participants suggest that the constant can be derived from the factorial of the leading coefficient multiplied by the degree of the polynomial. The conversation highlights the need for repeated differences to understand the relationship between the function values and their differences. Despite some guidance, the original poster still struggles to formulate a definitive equation. The thread emphasizes the importance of recognizing patterns in finite differences for polynomial functions.
Meh
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Hello there...I'm currently stuck with a problem regarding finite differences. The question asks for me to come up with an equation to find the constant of the finite difference. An example would be...Let's take the equation y=10x^4 and the constant is 240. Any hints as to where to start or anyone feeling generous enough to just give me the equation? o:)
 
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well, I don't have any proof of this in hand but you could notice that
10 * 4 * 3 * 2 * 1 = 240
 
I think what you are doing is finding repeated differences:

x f(x) \Delta x \Delta^2 x
1 10 150
2 160 640
3 810 1750 1940
4 2560 3690
5 6250
 
Thank Orthodontist and HallsofIvy, I think Ortho is on the right track...Still having a problem with coming up with an equation.
 

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