We define the multiplicty of the zero of a function f by the lowest power term in the Taylor series of the function about that zero.
2.
One derivation shows it is a special case of Newton's method ( also called the Newton-Raphson method ) for finding zeros of a function f ( x ) beginning with an initial guess.
3.
In any case, I think it's generally much easier to find the zero of a function then the max, which is why I found w ( n + 1 ) / w ( n ) above.
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