t, c, k = scipys_spline_representation
dt = t[k + 1:-1] - t[1:-k - 1]
d = (c[1:-1 - k] - c[:-2 - k]) * k / dt
t2 = t[1:-1]
d = np.r_[d, [0] * k]
new_spline_repr = t2, d, k - 1
finding inflection points in spline fitted 1d data