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本文将综合应用导数概念及解析几何的有关知识去解决有关曲线切线的几个问题,其中包括曲线及其切线间的关系,两曲线切线间的相互关系,两曲线相切等。目的在于使中学生将所学的解析几何知识与微积分知识联系起来,综合应用,从而学会解决解析几何中涉及曲线切线的一类综合题的思路与方法。本文所选例题,一般不超过近几年高考题的水平,有些题目,实际上就是近年高考题的变形与发展。因此,也可供教师在毕业生综合复习时作为参考。
This article will apply the concept of derivative and related knowledge of analytical geometry to solve several problems related to the tangent of the curve, including the relationship between the curve and its tangent, the relationship between the tangents of the two curves, and the tangency of the two curves. The purpose is to enable middle school students to connect the learned analytical geometry knowledge with the knowledge of calculus and apply them comprehensively, so as to learn to solve the ideas and methods of a comprehensive problem concerning the tangent of the curve in analytic geometry. The examples selected in this article generally do not exceed the level of the college entrance examination questions in recent years. Some of the topics are actually the distortions and developments of recent college entrance examination questions. Therefore, it can also be used as a reference for teachers in the comprehensive review of graduates.