...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

The examples demonstrate how to use the various tools for root finding.

We start with the simple cube root function `cbrt`

( C++ standard function name cbrt)
showing root finding without
derivatives.

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).

Then we show how a higher root (fifth
root) ^{5}√ can be computed, and in root_finding_n_example.cpp
a generic method for the nth
root that constructs the derivatives at compile-time.

These methods should be applicable to other functions that can be differentiated easily.