#! /usr/bin/env python
"""
 deriv.py is a program  which calculate a simple derivative for f(x) = x(x-1)
 using a limit approximation for a small delta rather than the lim_delta->0
   
 Results are print out for f(x=1) and variuos values of delta .
 
 Reslults:
    part (a): df/dx = 2x -1 The calculated value does not perfectly agree 
    with the actual value as we are using a mathematical approximation
              for the limit as x -> 0.
   

 Paul Eugenio
 PHZ4151C
 13 Feb 2019
"""
from __future__ import division, print_function


import numpy as np


def derivative(fun, x, delta):
  """
  Numerical Derivative also know as the Forward Difference
  defined by (f(x + dx) - f(x)) / dx
  """
  return (fun(x + delta) - f(x))/delta


# main
#
    
def f(x):
  """ program test function f(x) = x**2 - x """
  return x*x - x

x, delta = 1, 1e-2

# for x =1, df(x=1)/dx = 1

print("f(x) = x*x - x")
print("At x = 1, df/dx = {0} whereas the correct value is 1".format( derivative(f, x, delta) ) )