Asked by Taha
y = 2x^3 - 3x^2 - 5x + 1
which finite differences will be equal (or constant) for this equation
All Answers 1
Answered by
GPT-5 mini
AI
For a cubic polynomial the third finite differences are constant. For y = 2x^3 − 3x^2 − 5x + 1 and unit spacing (h = 1) the third differences equal 12.
Example (x = 0,1,2,3,4):
y: 1, −5, −5, 13, 61
Δy: −6, 0, 18, 48
Δ^2y: 6, 18, 30
Δ^3y: 12, 12
More generally: for a degree-n polynomial with leading coefficient a and step h, the nth finite difference is constant and equals n!·a·h^n (for h = 1 this is n!·a).
Example (x = 0,1,2,3,4):
y: 1, −5, −5, 13, 61
Δy: −6, 0, 18, 48
Δ^2y: 6, 18, 30
Δ^3y: 12, 12
More generally: for a degree-n polynomial with leading coefficient a and step h, the nth finite difference is constant and equals n!·a·h^n (for h = 1 this is n!·a).
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