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Interpolation problem
Ok so in school I have just recently begun doing interpolation. I am having a problem deriving a 2nd order polynomial when I am given two points and a evaluated derivative. For instance, given q(0)=-1, q(1)=-1, and q'(1)=4. I know how to do it when I have 3 points, but the q' presents me with a problem I am struggling with. Any help is appreciated thanks in advance.
SGS |
#2
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Re: Interpolation problem
[ QUOTE ]
Ok so in school I have just recently begun doing interpolation. I am having a problem deriving a 2nd order polynomial when I am given two points and a evaluated derivative. For instance, given q(0)=-1, q(1)=-1, and q'(1)=4. I know how to do it when I have 3 points, but the q' presents me with a problem I am struggling with. Any help is appreciated thanks in advance. SGS [/ QUOTE ] q(x) = Ax^2 + Bx + C q'(x) = 2Ax + B q(0) = C = -1 q(1) = A + B + C = -1 q'(1) = 2A + B = 4 subtracting q(1) from q'(1) gives A - C = 5 A - (-1) = 5 A = 4 => B = -4 q(x) = 4x^2 - 4x - 1 |
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