
06361442
j
2014f.00743
Stupel, Moshe
Fraivert, David
Oxman, Victor
Investigating derivatives by means of combinatorial analysis of the components of the function.
Int. J. Math. Educ. Sci. Technol. 45, No. 6, 892904 (2014).
2014
Taylor \& Francis, Abingdon, Oxfordshire
EN
I45
properties of highorder derivatives
zeroing of derivatives
composite functions
doi:10.1080/0020739X.2013.872306
Summary: Given a composite function of the form $h(x) = f(g(x))$, difficulties are often encountered in calculating the value of the $n$th derivative at some point $x = x_{0}$ when one attempts to determine whether its $n$th derivative becomes zero at this point, or attempts to find the sign of the $n$th derivative by differentiating it $n$ times and substituting $x_{0}$.{ }This present paper offers an alternative method that allows the investigation of the $n$th derivative of function $h(x)$ based on the investigation of functions $f(x)$ and $g(x)$ only.{ }Several examples are given, which implement the conclusions on the properties of the relation.