# Illustrating the concept of numerical differentiation 
# The function to be differentiated is f(x) = x**3 
# The derivative of the function is 3 x**2
# At x = 2, the derivative is therefore 12
#
# The purpose of this script is to show that if 
# delta is small, then the derivative can be 
# approximated by 
# (f(x+delta)-f(x))/delta

# Three different values of delta 
delta_list = [0.1,0.01,0.001]

# The value of x 
x = 2

# To calculate the approximate derivative for each value
# delta 
derivative_app = [ ((x + d)**3 - x**3)/d for d in delta_list]

# To display the approximate derivative 
for k in range(0,len(delta_list)):
    print('For d = {0:0.3f}: approximate derivative = {1:0.8f}'
          .format(delta_list[k],derivative_app[k]))