Search for inflection points in a spline

I have some one-dimensional data and put it with a spline. Then I want to find the inflection points (ignoring the saddle points). Now I am looking for extremes of my first output using scipy.signal.argrelmin (and argrelmax) for the set of values ​​generated by splev.

import scipy.interpolate
import scipy.optimize
import scipy.signal
import numpy as np
import matplotlib.pyplot as plt
import operator

y = [-1, 5, 6, 4, 2, 5, 8, 5, 1]
x = np.arange(0, len(y))
tck = scipy.interpolate.splrep(x, y, s=0)

print 'roots', scipy.interpolate.sproot(tck)
# output:
# [0.11381478]

xnew = np.arange(0, len(y), 0.01)
ynew = scipy.interpolate.splev(xnew, tck, der=0)

ynew_deriv = scipy.interpolate.splev(xnew, tck, der=1)

min_idxs = scipy.signal.argrelmin(ynew_deriv)
max_idxs = scipy.signal.argrelmax(ynew_deriv)
mins = zip(xnew[min_idxs].tolist(), ynew_deriv[min_idxs].tolist())
maxs = zip(xnew[max_idxs].tolist(), ynew_deriv[max_idxs].tolist())
inflection_points = sorted(mins + maxs, key=operator.itemgetter(0))

print 'inflection_points', inflection_points
# output:
# [(3.13, -2.9822449358974357),
#  (5.03,  4.3817785256410255)
#  (7.13, -4.867132628205128)]

plt.legend(['data','Cubic Spline', '1st deriv'])
plt.plot(x, y, 'o',
        xnew, ynew, '-',
        xnew, ynew_deriv, '-')
plt.show()

But that seems terribly wrong. I think there is an opportunity to find what I am looking for without generating so many values. Something like sproot, but applicable to the second output, maybe?