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2015年新课标全国卷Ⅰ(文科)第21题,是一道在函数、导数及不等式等知识交汇处命题的综合性问题,看似简单,却颇有味道,极具教学价值.现将笔者的思考历程及教学设计展示如下,希望抛砖引玉,得到大家的共鸣与讨论.题目设函数f(x)=e~(2x)-alnx.(1)讨论f(x)的导函数f′(x)的零点的个数;(2)证明:当a>0时,f(x)≥2a+aln2/a.此题只要突破了第(1)问,第(2)则迎刃而解,在此只分析第(1)问.1标准答案的困惑命题者提供的标准答案是(记为法1):法1函数f(x)的定义域为(0,+∞),
2015 New Curriculum Volume I (Arts) Question 21, is a comprehensive question in the function, derivative and inequality and other knowledge interchange proposition, seemingly simple, but quite flavor, very teaching value. (X) = e ~ (2x) -alnx. (1) Discuss the derivative function f ’(x) of f (x) ) (2) Proof: When a> 0, f (x) ≥2a + aln2 / a. As long as the problem breaks through the first (1) asked, the first (2) Analysis of (1) Q.1 Confusion of standard answers The standard answer provided by the proponent is (denoted as method 1): Method 1 The function f (x) has a domain defined as (0, + ∞)