In the context of cubic splines, the authors have contributed to a recent paper dealing with the computation of nonlinear derivatives at the interior nodes so that monotonicity is enforced while keeping the order of approximation of the spline as high as possible. During the review process of that paper, one of the reviewers raised the question of whether a cubic spline interpolating monotone data could be forced to preserve monotonicity by imposing suitable values of the first derivative at the endpoints. Albeit a negative answer appears to be intuitive, we have found no results regarding this fact. In this short work we prove that the answer to that question is actually negative.

翻译：在三次样条的背景下，作者曾参与一篇近期论文，该论文研究了内部节点处非线性导数的计算，以实现单调性保持，同时尽可能保证样条逼近阶数。在该论文的评审过程中，一位审稿人提出疑问：是否可以通过在端点处施加合适的一阶导数值，强制使插值单调数据的三次样条保持单调性？尽管直觉上答案似乎是否定的，但我们未发现关于此事实的任何已有结果。在这篇简短工作中，我们证明该问题的答案实际上是否定的。