Root Finder

#-------------------------------------------------------------------------------
# Name:        RootFinder.py
#
# Author:      Arjol Panci
#
# Created:     05-04-2020
#-------------------------------------------------------------------------------
import math

def falsePosition(xu, xl, fxu, fxl):
    return xu - ((fxu)*(xl-xu))/(fxl-fxu)

def findRootFalsePosition(f, xu, xl):
    fxu = f(xu)
    fxl = f(xl)
    xr = falsePosition(xu, xl, fxu, fxl)
    fxr = f(xr)
    while abs(fxr) > 0.00001:
        xr = falsePosition(xu, xl, fxu, fxl)
        fxr = f(xr)
        if abs(fxr) < 0.00001:
            return xr
        if ((fxr>0 and fxu>0) or (fxr<0 and fxu<0)):
            xu = xr
            fxu = fxr
        elif ((fxr>0 and fxl>0) or (fxr<0 and fxl<0)):
            xl = xr
            fxl = fxr
    return xr

def findRootNewton(f, x0):
    fx0 = f(x0)
    while(abs(fx0) > 0.00001):
        x0 = x0 - (fx0/derivativeApprox(x0, 0.0000000001, f))
        fx0 = f(x0)
    return x0

def derivativeApprox(x, dx, f):
    return (f(x+dx) - f(x))/(dx)

def f(x):
    return x**2-1 + math.log(x+1)

def f2(x):
    return math.log(1+x)*math.sin(x) + x**3 + 2*(x**2) - x - 2

def f3(x):
    a = (x)*((1+x)**35)
    return 24/x - 24/a - 140

print(findRootFalsePosition(f, 0, 1))
print(findRootNewton(f, 1))
print(findRootFalsePosition(f2, 0, 1))
print(findRootNewton(f2, 1))

print(findRootNewton(f3, 0.16))