The examples demonstrate how to use the various tools for root finding.
We then show how use of derivatives can improve the speed of convergence.
(But these examples are only a demonstration and do not try to make the ultimate
improvements of an 'industrial-strength' implementation, for example, of
boost::math::cbrt, mainly by using a better computed
initial 'guess' at cbrt.hpp).
These methods should be applicable to other functions that can be differentiated easily.