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导数是研究函数的单调性、极值、最值和值域与函数图像的强有力工具,导数的应用是新教材高考试题的热点,但因同学们学习中容易忽视相关概念的内涵和外延而导致应用错误。下面汇集解导数应用问题常见的错误,分析解答时的错解,充分暴露其错误的思维过程和出错的原因,旨在帮助同学们提高解题准确率。一忽视函数定义域就诊问题1:求函数f(x)=x-lnx的单调区间。错解症状:原函数求导可得f’(x)=1 11x
Derivative is a powerful tool to study the monotonicity, extreme value, maximum value and range of function and function image. The application of derivative is a hot topic in the new textbook examination questions, but it is easy for the students to neglect the connotation and extension of related concepts. Cause application error. The following summarizes common mistakes in solving derivative application problems, analyzes the mistakes in the answers, and fully exposes the wrong thinking process and the causes of mistakes, in order to help students improve the accuracy of problem solving. Ignoring the Function Definition Domain Visit Problem 1: Find the monotonic interval of the function f(x)=x-lnx. Misunderstood symptoms: the original function derivation available f’(x) = 11x