def quartic ( x ):

#*****************************************************************************80
#
## quartic evaluates the quartic function.
#
  f = 2.0 * x ** 4 - 4.0 * x ** 2 + x + 20.0

  return f

def quartic_df ( x ):

#*****************************************************************************80
#
## quartic_df evaluates the derivative of the quartic function.
#
  df = 8.0 * x ** 3 - 8.0 * x + 1.0

  return df