The file attached shows the results of using a spline curve that seems to breakdown over a certain region. Can anyone tell me why that region is so special and why using the Newton-Raphson method could yield these results?

Columns A and B represent the (x,y) data for a calibration curve. See plot of spline curve. The curve is generated by calculating y = ax^3 + bx^2 +cx + d, where the spline coefficients a, b, c, and d are used over certain regions (color-coded for clarity). For example, for x = 0 to 100, use the 1st row of coefficients, for x = 100 to 500, use the 2nd row, etc.

Columns E anf F represent the actual calibration (x,y) data that are used to generate the spline coefficients in Columns J through M.

Column C represents the values for x when using the Newton-Raphson method for the corresponding y value. Notice that everything is fine up until x =364. From x = 372 to x = 500, the Newton-Raphson method "blow up". For values greater than x = 500 the Newton-Raphson method is normal.

So, what causes the "blow-up. What is so special about those particular values of y using the appropriate set of coefficients?

Thanks for any insight as this is driving me crazy.