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flyingheadlice
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This is a problem from the book section about Newton's Divided Differences, but I don't see how it really connects to the chapter other than that you draw out the triangle diagram.
Define $P(x) = P(x+1)-P(x), where P is an unknown 4th degree polynomial
and that
$^2P(x) = $($P(x)) = $(P(x+1)-P(x)) = $P(x+1) - $P(x) = P(x+2) -2(P(x+1) +P(x))
Given $^2 P(0) = 0, $^3 P(0) = 6, $^4 P(0) = 24
Find $^2 P(10)
I used a4x^4 + a3x^3 + a2x^2 + a1x +a0 = Pn(x) and plugging in the givens I got that:
a4 = 1, a3 = -5, a2 = -8, but I wasn't able to get a1 and a0 because they cancel out each time. I am not sure if I need a1 and a0 to find $^2 P(10), or if there is another way to do it.
Thanks in advance for any help.
Homework Statement
Define $P(x) = P(x+1)-P(x), where P is an unknown 4th degree polynomial
and that
$^2P(x) = $($P(x)) = $(P(x+1)-P(x)) = $P(x+1) - $P(x) = P(x+2) -2(P(x+1) +P(x))
Given $^2 P(0) = 0, $^3 P(0) = 6, $^4 P(0) = 24
Find $^2 P(10)
Homework Equations
The Attempt at a Solution
I used a4x^4 + a3x^3 + a2x^2 + a1x +a0 = Pn(x) and plugging in the givens I got that:
a4 = 1, a3 = -5, a2 = -8, but I wasn't able to get a1 and a0 because they cancel out each time. I am not sure if I need a1 and a0 to find $^2 P(10), or if there is another way to do it.
Thanks in advance for any help.