code: def test_newton(self):
      for f, f_1, f_2 in [
          (self.f1, self.f1_1, self.f1_2),
          (self.f2, self.f2_1, self.f2_2),
      ]:
          x = zeros.newton(f, 3, tol=1e-6)
          assert_allclose(f(x), 0, atol=1e-6)
          x = zeros.newton(f, 3, x1=5, tol=1e-6)  # secant, x0 and x1
          assert_allclose(f(x), 0, atol=1e-6)
          x = zeros.newton(f, 3, fprime=f_1, tol=1e-6)  # newton
          assert_allclose(f(x), 0, atol=1e-6)
          x = zeros.newton(
              f, 3, fprime=f_1, fprime2=f_2, tol=1e-6
          )  # halley
          assert_allclose(f(x), 0, atol=1e-6)
  
imports: import pytest
  from math import sqrt, exp, sin, cos
  from functools import lru_cache
  from numpy.testing import assert_warns, assert_, assert_allclose, assert_equal, assert_array_equal, suppress_warnings
  import numpy
  from numpy import finfo, power, nan, isclose
  from scipy.optimize import zeros, newton, root_scalar
  from scipy._lib._util import getfullargspec_no_self
  from scipy.optimize._tstutils import get_tests, functions, fstrings
label_desc: Use image node_id 20 for calling the TestBasic obj's underlying member method code with example usage: obj.test_newton() without return types