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应用函数的单调性定义论证函数的单调性是高中数学教学训练中的一项基础工作．现行教材由于导数的引入,使得近年高考试卷中以三次函数为载体、以考察函数单调性为核心的函数综合题成为命题一大亮点．这些试题综合性强、难度大,命题者本意是考察导数知识的灵活应用．本文给出用单调性定义解决所有三次函数单调性的一种方法,能够成功地避开导数知识,使得这种难度较大的试题可以推向高一年级实施训练,让学生较早地接触、了解、熟悉三次函数及其基本性质,更有利于提高学生应用数学基础知识求解含参数问题的能力．
Monotonicity of Application Function Definition Monotonicity of argument function is a basic work in high school mathematics teaching and training. Due to the introduction of the derivative of the current teaching material, the function of the monotonicity of the function as the core of the examination paper in the college entrance examination papers in recent years as a carrier to make the subject a major bright spot. Comprehensive examination of these questions, difficult, proponents intended to study the derivative knowledge of the flexible application. In this paper, a method of solving the monotonicity of all cubic functions by monotonicity is given, which can avoid knowledge of derivatives successfully. This kind of difficult test can be put into practice in the first grade and students can get in touch with them earlier. To understand and be familiar with the cubic functions and their basic properties is more conducive to improving students’ abilities to solve problems with parameters by applying the basic knowledge of mathematics.