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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.