cancerous growths in the archetype

[spiny urchin]

This finds the intersection of a curve with the x-axis:

http://www.stonetabernacle.com/intersect-curve.html

The curve is drawn, all points derived and the tangent and normal to the
tangent are determined. Vector algebra is then applied between points on
the graph. From this it is shown that f '(x)=I Newton's Method is derived.
Newton's Method is extrapolated to the nth derivative of the nth degree
polynomial (such as n=1000). From there the smallest increment is used to
reconstruct the equation working backwards until the original is obtained.
All roots to the power series are obtained and the problem solved.

With this problem finally solved, it may prove a useful tool to disassemble
some of the mutant growths in the collective... and as usual, fall in the
hands of dissidents yearning to keep the mutant growths reigning and
continuing to assault. Peace be with them. So long.

[spiny urchin]

Case in fact. Consider the 7th degree polynomial. Six derivatives are
taken for the numerator, and seven derivatives are taken for the numerator.
Relatively taken, the result is just the same as a 0th derivative in the
numerator and the 1st derivative in the denominator:

f^6(x) ->f^0(x)
f^7(x) -> f^1(x)

that is,

x_c = x - (f^6)/(f^7) is the same as,
x_c = x - (f^0)/(f^1) per increment

where

f^1(x)=+/- I

This is to resolve the unknown trouble I've been to people, unknowingly how
with unknown results. These things are unknown.

Post by spiny urchin
http://www.stonetabernacle.com/intersect-curve.html
The curve is drawn, all points derived and the tangent and normal to the
tangent are determined. Vector algebra is then applied between points on
the graph. From this it is shown that f '(x)=I Newton's Method is
derived. Newton's Method is extrapolated to the nth derivative of the nth
degree polynomial (such as n=1000). From there the smallest increment is
used to reconstruct the equation working backwards until the original is
obtained. All roots to the power series are obtained and the problem
solved.
With this problem finally solved, it may prove a useful tool to
disassemble some of the mutant growths in the collective... and as usual,
fall in the hands of dissidents yearning to keep the mutant growths
reigning and continuing to assault. Peace be with them. So long.