函数观点解题新例

• 作 者: 崔宗和 罗增儒
• 机 构: 西安铁三中,陕西师大,
• 出 处: 数学教学通讯
• 发表日期: 1989年02期
• 关键词: 数学方法 凹凸性 数学内容 点对应 罗增 知沟 非负整数 奥林匹克竞赛 操作过程 次后

把所求解的问题转化为函数性质的讨论,再由函数的性质回答求解的问题,我们称为函数观点解题。这里的关键是,根据题目提供的信息,设计一个恰当的函数,这种设计,既是对数学内容的深刻理解,又是对数学方法的灵活运用,实在是内容与方法的完美统一。把一个不等式转化为函数单调性、凹凸性或极值的确定,是读者所熟知的,下面再提供几个新近的例子。

The problem solved is converted into a discussion of the nature of the function, and then the problem is solved by the nature of the function. We call it the function point of view. The key here is to design an appropriate function based on the information provided by the topic. This design is both a profound understanding of mathematical content and a flexible use of mathematical methods. It is the perfect unity of content and method. Transforming an inequality into the determination of the monotonicity, asperity, or extremum of a function is well known to the reader. Here are a few more recent examples.