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第二节：参考范文：Driving home,everyone was talking about their gifts in high spirits except the youngest daughter,Gin-ger.Feeling puzzled,Melissa asked what she had bought for Christmas."Nothing.Ginger whispered,lower-ing her head.Other kids stopped talking and turned to Ginger."Are you kidding?Did you lose your money?"They stared at the little girl,their faces lighting up with surprise.Ginger shook her head and said that she gavethe bill to a man who was begging outside the supermarket.The man in rags was standing in cold weather.There was no doubt that he was homeless and had a hard time."We have so much,but the homeless man doesn't have anything,"Ginger explained."I am willing to sharemy happiness with him.I hope he can buy warm clothes or treat himself to a good dinner."She added,witheyes shining with excitement.Hearing her daughters'words,Melissa felt a sense of pride swept through her."What you did is right,Ginger.You are such a kind child that we are proud of you,"she said.Arriving home,they had a small party and the other kids offered to share their gifts with Ginger.It was the special experiencethat made the kids realize sharing is important.

(1)解：由函数f(x)=1nx-mx,得f'(x)=1-m=1-m严(x>0),(1分)①当m≤0时，f'(x)>0,则f(x)在区间(0，十∞)上单调递增，至多有一个零点；(2分)②当m>0时，0 0,则f(x)在区间(0，)上单调递增mx>上时，f(x)<0,则f(x)在区间（品，十∞）上单调递减，(4分)n所以f)在x=之处取得最大值，中f)=-1nm-1>0,解得0 2>e>1,而f)=-m<0,f()=-2nm-<0,此时m2m所以由零点存在性定理可知，x)在区间(1，)和（元）上各有一个索点，(5分)综上所迷，m的取值范国是(0，)(6分)(2)证明：因为x1,x2是f(x)的两个零点，不妨设x1>x2>0,所以lnx1-mx1=0①，lnx2-mx2=0②，(7分)①-②得lnx1-lnx2=mx1-mx2,即m=In x-In x2(8分)x1-x2由f'(x)=-m,得f'x1十x,)=1-m=1n二n,(9分)x1十x2x1十x2x1一x2要证f'(x1十x2)<0,即证正nx1nx2>。1,即证lnx1-lnx2>+x2'x1一x2x1十x2x1-1即证ln1-x?一>0，即证ln+0x2x1十12-1>0.nx21十1(10分)T2I2经=>1，设p0)=n+异一1(11分)Tp'(t)=t2+1t(t+10>0,所以p(t)在t∈(1，+∞)时单调递增，则(t)>p(1)=0,即f'(x1十x2)<0得证.(12分)