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zuluuu0

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Help on question on not-a-knot condition

Help with this question would be greatly appreciated.
The not-a-knot condition for obtaining the remaining equation/conditions in the system of equations for the yi is accomplished by requiring that S'''(x) be continuous at points x1 and x(n-1).
Find the resulting end condition equations in this case, where
yi' = S'(xi),    i = 0(1)n.
Si(x) = fi + yi'(x - xi) + ai(x - xi)^2 + ci(x - xi)^2(x - x(i+1))
for x in [xi, x(i+1)].
Where ai and ci are constants on the interval.

Thanks in advance.