22.本题考查利用导数研究函数的单调性与最值,零点存在性定理的应用(1)【解】当a=0时f(x)=2lnx-x2-1,则f"(x)=2(x+1)(x-1)0(根据已知条件写出f(x),并求出f"(x),要特别注意函数的定义域为(0,+∞),此条件是解答本题的关键所以当0 0,此时函数f(x)单调递增当x>1时(x)<0,此时函数f(x)单调递减综上,函数f(x)在区间(0,1)上单调递增,在区间(1,+∞)上单调递减(2)【证明】由题意可得/=2+4-2x=-2(x2-2ax-1x>0,令f'(x)=0,解得x=a±√a+1(求出∫'(x),根据函数∫(x)的定义域确定当∫'(x)=0,即函数f(x)取得极值时x的值,结合“f(x)=0有且只有一个实数解”可得∫"(x0)=0且f(x0)=0)因为a>0,所以x=a+√a2+1>1,x=a-√a2+所以f'(x)在(1,+∞)上有唯一零点x=a+√a2+1当x∈(1,x)时f'(x)>0,f(x)在(1,x)上单调递增;当x∈(x0,+∞)时f(x)<0,fx)在(x,+∞)上单调递减所以f(x)=、=f(x0)因为f(x)≤0在(1,+x)上恒成立,且f(x)=0有且只有一个实数解,所以rf'(x)=0+4a-2即{x0f(x0)=02lnx0+4ax0-x2-1=0,消去a并整理得2lnxo+x2-3=0.(通过构造新函数,利用导数研究新函数的单调性,结合零点存在性定理,即可求出x的取值范国,必+40-2x0=0分离参数a,借助函数的单调性即可证明结论成立)令A(x)=2lnx+x2-3,则h(x)=2+2x,x>0,h'(x)>0在(1,+∞)上恒成立,所以h(x)在(1,+∞)上单调递增,又h(1)=-2<0,h(2)=2hn2+1>0,所以1

第二节【写作提示】1.审题:(1)明确故事人物:本故事中主要人物为格林一家:母亲埃米、父亲艾伦、女儿阿比以及电力工人迈克:(2)厘清主要事件:疫情期间,格林一家在外出时买了一个风筝,女儿阿比在放风筝时遇到大风,风筝被吹到了电线上。无奈之下,埃米向国家电网求助,随后电力工人迈克赶到并成功取下风筝,但风筝因与电线缠绕太紧而损坏了。送还风筝后,迈克发现阿比伤心地将风筝埋在了后院,深受触动的他决定做点什么。2.写作要点根据已知人物、事件及续写段落开头语可推测故事发展:第段开头语为第二天,艾伦像往常一样去取邮件”;第二段开头语为“艾伦被这个善举深深地感动了,他把整个故事发到了网上。因此续写部分第一段可描写艾伦取邮件后发生的事情,邮件内可能与迈克所做的善举有关;第二段可描写故事被分享到网上后的影响【参考范文】The next day, Alan went out to gef the mail as usual. To hissurprise, there was a new kite--a cute robin with beautiful featherg-inthe box along with a note written on the National Grid s notepaper."I feltbad for your daughter, so I hope this new kite could make her smile,itread."Stay safe and healthy ! The nole was unsignedDeeply moted by this act of kindness, Alan posted the whole story onthe Internet. Soon, word got back to National Grid, which quicklyidentified Mike, the worker who had carefully saved the kite from thwires. He told that as he saw Abbey burying the kite, he thought of hisown little sister and knew it well that the girl must be extremely sad. Soafter he left the Greens's house for more service calls that afternoon, hestopped by a shop to buy the new kite and sent it to the family. He didntexpect to be recognized, but Alan's post led to his identity beingrevealed, which resulted in the story being shared and liked by millions ofpeople throughout the Internet【点评】本文续写详略得当,情节合理。第一段内容承接段首所给开头语,主要讲述了艾伦取邮件时发现了一个新的风筝,并且附有一张匿名的纸条,纸条上表达了希望艾伦的女儿能因为这个新风筝而感到快乐以及对艾伦一家的祝福,这与原文中的 he decided to dosomething相呼应,同时也与第二段开头语中的 this act of kindnes完美衔接。第二段主要讲述艾伦将这个故事发布到网上以后,国家电网丑速找出了这位不留名的好心人迈克,迈克说自己原本不想透露姓名,但因为艾伦的帖子,他的故事在网上被数百万人分享。范文中不乏高级词汇和句式,如 to one' s surprise, along with, reveal, result in以及过去分词短语作定语、whch引导的定语从句、that引导的宾语从句等,为文章增色不少。

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