#! /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): the calculated value does not perfectly agree with the 
              actual value as we are using a mathematical approximation
              for the limit as x -> 0.
    part (b): The accuracy get better because the mathematical approximation
              improves for smaller delta, but it eventually gets worst due to 
              computational round off and subtractive cancellation errors.

 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 = 1
# for x =1, df(x=1)/dx = 1
print("delta","df/dx",sep='\t')
for i in range(2,20,2):
    delta = 10**(-i)
    print( delta, derivative(f, x, delta),sep='\t')