code: def test_three_points(self):
      # gh-11758: Fails computing a_m2_m1
      # In this case, s (first derivatives) could be found manually by solving
      # system of 2 linear equations. Due to solution of this system,
      # s[i] = (h1m2 + h2m1) / (h1 + h2), where h1 = x[1] - x[0], h2 = x[2] - x[1],
      # m1 = (y[1] - y[0]) / h1, m2 = (y[2] - y[1]) / h2
      x = np.array([1.0, 2.75, 3.0])
      y = np.array([1.0, 15.0, 1.0])
      S = CubicSpline(x, y, bc_type="periodic")
      self.check_correctness(S, "periodic", "periodic")
      assert_allclose(
          S.derivative(1)(x), np.array([-48.0, -48.0, -48.0])
      )
  
imports: import warnings
  import io
  import numpy
  from numpy.testing import assert_almost_equal, assert_array_equal, assert_array_almost_equal, assert_allclose, assert_equal, assert_
  from pytest import raises
  from scipy.interpolate import KroghInterpolator, krogh_interpolate, BarycentricInterpolator, barycentric_interpolate, approximate_taylor_polynomial, CubicHermiteSpline, pchip, PchipInterpolator, pchip_interpolate, Akima1DInterpolator, CubicSpline, make_interp_spline
label_desc: Use image node_id 7 for calling the TestCubicSpline obj's underlying member method code with example usage: obj.test_three_points() without return types