symdiff <- function ( f, x, h = x * .Machine$double.eps^(1/3) )

#*****************************************************************************80
#
## symdiff applies the symmetric finite difference formula to a function.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    03 March 2020
#
#  Author:
#
#    Original R code by James Howard;
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017,
#    ISBN13: 978-1-4987-2363-3.
#
{
  dfdx = ( f ( x + h ) - f ( x - h ) ) / 2.0 / h

  return ( dfdx )
}