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Full Version: How to find the first negative derivative ?
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Sign theory

Consider f(x) = 0 + A1 x + A2 x^2 + ...

Where f is entire and all n th derivatives are positive.
Also f(x) > x for x > 0 and the fixpoint at 0 is hyperbolic.
Also there are no there are no other fixpoints within or on the unit radius.

Now use the usual method to find the half iteration g(x).

How to efficiently find the first n th derivative ( Of g(x) at x = 0 ) < 0 ??