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导数作为高中新教材的新增内容之一,它给高中数学增添了新的活力,特别是导数广泛的应用性,为我们展现出一道亮丽的风景线,也使它成为新教材高考试题的热点和命题新的增长点．为此,本文从以下几个方面介绍导数在解题中的应用．一、应用导数求切线例1 已知抛物线C1:y=x2+2x和抛物线C2:y=-x2+a,当a取什么值时,C1和C2有且仅有一条公切线?写出公切线的方程．分析:传统的处理方法是用“△”法来解决, 但计算量大,容易出错．如能运用导数的几何意义去解,则思路清晰,解法简单．
Derivatives as one of the new content of new high school textbooks, it adds a new vitality to high school mathematics, especially the wide range of derivative applicability, showing us a beautiful landscape, but also make it a hot topic for the new textbook entrance exam questions Proposition new growth point. For this reason, this article introduces the application of derivative in solving problems from the following aspects. First, apply the derivative of tangent line Example 1 known parabola C1: y = x2 + 2x and parabola C2: y = -x2 + a, when a take what value, C1 and C2 and has only one common tangent? Tangential equation. Analysis: The traditional method is to use the “△” method to solve, but the calculation of large, prone to error. If we can use the geometric meaning of the derivative to solve, the idea is clear, the solution is simple.