""""
Demo code from lecture on Sep 5th. Demonstrate
how a function can be passed as a function to
another function.
"""

"""
The function diff(...) estimates the derivative
of a function f in a point x. The first parameter
to the function is a Python function f.
From how f is used inside the function, we see that
it must be defined with a single parameter.
"""
def diff(f, x, h=1e-6):
    r = (f(x+h) - f(x)) / h
    return r

#define python function for a mathematical formula
def g(x):
    return x**2 - 2 * x

#call diff with g as the first argument
print(diff(g, x = 1.5))   
"""
Notice that there are no parantheses after g. We pass
the actual function, not the result of a function call.
"""

#alternative version using a lambda function:
print(diff(lambda x: x**2 - 2 * x, 1.5))

"""
Terminal> python func_argument.py 
1.0000009997845893
1.0000009997845893
"""