In this paper, we derive an optimal first-order Taylor-like formula. In a seminal paper [14], we introduced a new first-order Taylor-like formula that yields a reduced remainder compared to the classical Taylor's formula. Here, we relax the assumption of equally spaced points in our formula. Instead, we consider a sequence of unknown points and a sequence of unknown weights. Then, we solve an optimization problem to determine the best distribution of points and weights that ensures that the remainder is as minimal as possible.

翻译：本文推导了一种具有最优性的一阶类泰勒公式。在开创性论文[14]中，我们提出了一种新型一阶类泰勒公式，其产生的剩余项小于经典泰勒公式。本文放宽了该公式中基于等距点的假设，转而考虑未知点序列和未知权重序列。通过求解优化问题，我们确定了使剩余项尽可能最小的最优点分布与权重分配方案。