  The purpose of this letter is to investigate the time complexity consequences
of the truncated Taylor series, known as Taylor Polynomials
\cite{bakas2019taylor,Katsoprinakis2011,Nestoridis2011}. In particular, it is
demonstrated that the examination of the $\mathbf{P=NP}$ equality, is
associated with the determination of whether the $n^{th}$ derivative of a
particular solution is bounded or not. Accordingly, in some cases, this is not
true, and hence in general.
