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随着新课程改革的逐步深入,导数作为微积分的核心概念之一迅速成为考试热点。它不仅是一种重要的解题工具,而且还是初等数学与高等数学之间的一座桥梁。作为工具,导数在判断函数单调性、求函数极(最)值、证明不等式以及数列求和等问题中为我们提供了一种新的思路与方法。作为桥梁,导数使中学生能够提前接触到微积分知识,为其将来学习高等数学打下良好的基础。本文收集和分析了导数在高中数学若干典型问题中的应用。
With the gradual deepening of the new curriculum reform, the derivative as a core concept of calculus quickly become a hot topic. It is not only an important problem-solving tool, but also a bridge between elementary and advanced mathematics. As a tool, the derivative provides a new way of thinking for us in judging the monotonicity of the function, finding the pole (most) value of the function, proving the inequality and the summation of the series. As a bridge, derivatives lead middle school students to gain advance knowledge of calculus and lay a good foundation for their study of advanced mathematics in the future. This paper collects and analyzes the application of derivatives in several typical high school math problems.