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导数是中学数学教材的新增内容,它是高等数学的基础内容之一。导数的出现给中学数学带来了新的活力,是高考命题的热点。但由于导数是中学数学的选修内容,要求相对较低,因此,教材所配置的习题也比较简单。使得在教学中一些比较容易辨析清楚的概念及基本知识之间的联系往往变得模糊不清,如曲线切线的概念,连续与可导、区间上导数的符号与函数单调性、极值点与导数为零的点等之间的联系,出现失误。
Derivatives are the new content of middle school mathematics textbooks. It is one of the basic contents of higher mathematics. The appearance of derivatives has brought new vitality to middle school mathematics, and it is a hot spot for college entrance examination propositions. However, because the derivative is an optional content for middle school mathematics, the requirements are relatively low. Therefore, the exercises for the teaching materials are relatively simple. It makes the links between some concepts and basic knowledge that are more easily discerned in teaching, such as the concept of curve tangents, the monotonicity of the symbols and functions of the continuous and derivative, interval derivatives, and the extremum points. Links between points where the derivative is zero, errors occur.