导数是高中数学与大学数学的一个连接点,一方面它为中学研究函数的性态提供了有力的工具,另一方面它也是大学微积分的核心概念之一,是进一步学习微积分的基础.从高等数学的观点看,导数之所以成为高中阶段解决函数不等式及函数其他相关问题的基本方法的一个潜在原因,缘于高中阶段题目中的函数类型主要由二次函数、指数函数、对数函数以及三角函数等基本初等函数构成,或者由这些基本初等函数进行四则运算,复合而成,上述初等函数或初等函数复合而成的函数在其定义域区间上是“可导”的,这就为分析函数的单 Derivatives is a connection point between high school mathematics and university mathematics. On the one hand, it provides a powerful tool for studying the state of function in high school. On the other hand, it is also one of the core concepts of university calculus. Derivatives are the basis for further studying calculus. From a higher mathematics point of view, the reason why the derivative becomes a potential reason for solving the basic method of function inequality and other related problems in high school is that the type of the function in the high school topic is mainly composed of quadratic function, exponential function, logarithmic function And basic functions such as trigonometrical functions, or by the basic elementary functions of the four operations, compound, formed by the primary function or elementary functions of the composite function in the domain of its definition is “conductive ”, which Just analyze the function of the single