题目

已知函数f（x）=2acos2x+bsinxcosx,且f(0)=2,f()=.（1）求f（x）的周期,最大值以及取得最大值时对应的x值；（2）求f（x）的单调区间. 答案：解：（1）由f(0)=2a=2,得a=1,f()=a+b,得b=2,∴f(x)=2cos2x+2sinxcosx=sin2x+cos2x+1=sin(2x+)+1.∴f（x）的周期是T=π.当2x+=2kπ+,即x=kπ+(k∈Z)时,f（x）最大值是+1. （2）求减区间:2kπ+≤2x+≤2kπ+,2kπ+≤2x≤2kπ+,kx+≤x≤kπ+,∴减区间为［kπ+,kπ+］,k∈Z. 求增区间:2kπ-≤2x+≤2kπ+,kπ≤x≤kπ+,即增区间为［kπ,kπ+］,k∈Z.假如你是李华，你们学校上周开展了以“建设绿色校园”为主题的实践活动。请你用英语写一篇短文投稿，谈谈在活动中你做了什么，你的感受以及保护环境的重要性。提示词语：water the trees and flowers, collect the waste, happy, important提示问题：●What did you do in the activity?●How did you feel after the activity?●What do you think of protecting the environment?At my school, we held a practical activity about how to make a green school last week. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________