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等号.故好一4好的最小值为一1.(12分)21.【名师指导】本题考查利用导数研究函数的单调性、极值、最值，考查运算求解能力，考查转化与化归思想(I根据a<2时，f代x)≤是-x+21x,所以只需证g()=士-x+21x<0即可，对函数g(x)求导，根据函数的单调性证明g(x)≤0即可（Ⅱ）对了(x)求导，根据x,为∫(x)的极值点，结合根与系数的关系可得王与x十的值，根据函数的定义求出()一f八)的表达式，再构造函数h(x)=f(x)一f(x),对h(x)进行求导研究其单调性，进而得出h(x)的最大值，即得∫()一f()的最大值.解：(I)证明：当x∈[1，+oo)时，lnx>0,故当a<2时，x) <左-x+2lnx,所以只需证g(田)=-x十21nr<0即可.因为8)=--1+2=-2-=-d≤0.所以g(x)在(0，+∞)上单调递减，而g(1)=0,所以当x∈[1，十∞)时，有g(x)≤0，即当x∈[1，+0)时，f(x)≤0成立.(5分)( a的定义被为0，+o),fx)="-号-1+是=-二a+1,所以当"> 号时，2-ax十1=0有两个正根，即)存在两个极值点.由于f(x)的两个极值点，满足方程x2一ax十1=0，所以=1，西十=8，则有马十士=>号由 <解得0<<号由马<，解得0<<2)-gr )+alnralntit="+-十alh号TI" i:="2(-)+(十x)ln=2-)+2(+五h,'令A()=2(-x)+2(+x)lnx,0
第二节(满分25分[文])One possible versionTh[章]en came the Rajasthan[来] /v trip which was our official last trip I hanged out with my otherErie[自]iends while she with the other two girls. I wasn,t enjoying this trip at all, which she could makeBout.[知] When she saw me approachi[嘛]ng the common washroom,[答] she followed me in and shut thedoor. I didn 't know how to react. She gave me a tight hug and broke down. My tears were alsoout of control We knew we both wanted to be in each others company. We promised to growmatur[案]e and let it not affect our friendshi[网]paozIt's been almost 7 years after graduatio[文]n since we picked up our friendshi[章]p. Shes one of thefew people I really count on in my life. She's been with me through all my struggles[来], helping meconstan[自]tly to grow into a better individua[知]l. So have I. The only learning from our relations[嘛]hipis-if someone is meant to be in your life, they will ensure they stay around some way or theher Willingne[答]ss to keep a relations[案]hip should come from both the sides
