import math


#Newton Raphson metode
def derivertavX(f, x):
    return abs(f(x))

def NewtonRaphson (f ,derivertavF, start, e):


    stigning = derivertavX(f, start)

    while stigning > e:

        start = start - ((f(start))/(derivertavF(start)))
        stigning = derivertavX(f, start)

    return start


#oppgave1
def f(x):
    return x**3-3

def derivertavF(x):
    return 3*x**2

starts = [2.5]
for start in starts:
    xvariable = NewtonRaphson(f, derivertavF, 2.5, 2e-1)
    print (xvariable)

#oppgave 2

def g(x):
    return (5*x + math.log(x)-10000)

def derivertavG(x):
    return (5+ 1/x)

starts = [1,2000]
for start in starts:
    x2variable = NewtonRaphson(g, derivertavG, start, 1e-6)

print (x2variable)

#oppgave 3


def y(x):
    return 2 - x**2 - math.sin(x)


def derivertavY(x):
    return -2*x - math.cos(x)


def NewtonRaphson2(f, derivertavF, start):

    start = start - ((f(start)) / (derivertavF(start)))

    return start

start = 0

for val in range(5):
    newX = NewtonRaphson2(y, derivertavY, start)
    start = newX

print(start)



start = -2
for val2 in range(5):
    newX = NewtonRaphson2(y, derivertavY, start)
    start = newX

print(start)





#oppgave 4

def z(x):
    return x**2 - 10

def derivertavZ(x):
    return 2*x

for val in range(3):
    x4variable = NewtonRaphson(z, derivertavZ, start, 1.E-08)
    start = x4variable

x4variable = abs(x4variable)
print (x4variable)