#### Newton Method

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```"""Newton's Method."""

# Newton's Method - https://en.wikipedia.org/wiki/Newton%27s_method
from collections.abc import Callable

RealFunc = Callable[[float], float]  # type alias for a real -> real function

# function is the f(x) and derivative is the f'(x)
def newton(
function: RealFunc,
derivative: RealFunc,
starting_int: int,
) -> float:
"""
>>> newton(lambda x: x ** 3 - 2 * x - 5, lambda x: 3 * x ** 2 - 2, 3)
2.0945514815423474
>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -2)
1.0
>>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -4)
1.0000000000000102
>>> import math
>>> newton(math.sin, math.cos, 1)
0.0
>>> newton(math.sin, math.cos, 2)
3.141592653589793
>>> newton(math.cos, lambda x: -math.sin(x), 2)
1.5707963267948966
>>> newton(math.cos, lambda x: -math.sin(x), 0)
Traceback (most recent call last):
...
ZeroDivisionError: Could not find root
"""
prev_guess = float(starting_int)
while True:
try:
next_guess = prev_guess - function(prev_guess) / derivative(prev_guess)
except ZeroDivisionError:
raise ZeroDivisionError("Could not find root") from None
if abs(prev_guess - next_guess) < 10**-5:
return next_guess
prev_guess = next_guess

def f(x: float) -> float:
return (x**3) - (2 * x) - 5

def f1(x: float) -> float:
return 3 * (x**2) - 2

if __name__ == "__main__":
print(newton(f, f1, 3))
```