四川省内江威远自强中学高2016届数学（理）练习（30）（PDF版）

0fx??得1x?,??0,1x?时,??0fx??,??fx单调递增;??1,x? ??时,??0fx??,??fx单调递减.综上,??fx单调递增区间为??0,1,单调递减区间为??1,??.(2)????22122axg x axxx??? ??①当0a?时,??0gx??,单调递减,故不可能有两个根,舍去②当0a?时,10,xa?????????时,0)(??xg,)(xg单调递减,1,xa??? ????????时,0)(??xg,)(xg单调递增.所以11ga?????????得01a??.??????????)(,,)(,0xgxxgx,所以01a??(3)不妨设121xx??,由(1)知??1,x? ??时,??fx单调递减.????1 2 1 2ln lnf x f x k x x? ??,等价于??????2 1 1 2ln lnf x f x k x x? ??即????2 2 1 1ln lnf x k x f x k x? ??存在1x,??21,x? ??且12xx?,使????2 2 1 1ln lnf x k x f x k x? ??成立令????lnh x f x k x??,??hx在??1,??存在减区间??234ln0kx xhxx????有解,即24lnxkx?有解,即2max4lnxkx???????令??24lnxtxx?,????34 1 2lnxtxx???,??0,xe?时,)(,0)(xtxt??单调递增,[来源:]??,xe? ??时,)(,0)(xtxt??单调递减,2max4ln 2xxe???????,?2ke?.