3、<2.若f(x)的三个零点为x1,x2,x3,且x1-1B.x2<0C.x2>0D.x3>2【答案】C5..(浙江省杭州高中2013届高三第六次月考数学(理)试题)已知函数1x,x032f(x)x3x1,g(x)4x,则方程g[f(x)]a0(a为正实数)的根的个数不x26x8,x0可能为( )A.3个B.4个C.5个D.6个【答案】A6..(2013年普通高等学校招生统一考试浙江数学(理)试题(纯WORD版))已知为自然对数的底数
4、e,设xk函数f(x)(e1)(x1)(k1,2),则( )A.当k1时,f(x)在x1处取得极小值B.当k1时,f(x)在x1处取得极大值C.当k2时,f(x)在x1处取得极小值D.当k2时,f(x)在x1处取得极大值【答案】C二、解答题7..(浙江省五校联盟2013届高三下学期第一次联考数学(理)试题)已知函数112f(x)ln(ax)xax(a为常数,a0)22(1)当a1时,求函数f(x)在x1处的切线方程;1(2)当yf(x)在x处取得极值时,若关
5、于x的方程f(x)b0在0,2上恰有两个不相等的2实数根,求实数b的取值范围;12(3)若对任意的a(1,2),总存在x,1,使不等式f(x)m(a2a3)成立,求实数m的002取值范围.112【答案】(1)a1时,f(x)ln(x)xx22'1'3f(x)2x1,于是f(1),又f(1)0,即切点为(1,0)1x23切线方程为y(x1)2'a(2)f(x)2xa,1ax'1a10,即a2a,a0,a2f()a2
6、0211a2此时,'2x(2x1),1上减,1,2上增,f(x)x0,12x221135又f(0)ln,f(),f(2)ln224231bln42222a2ax(2a)xx2ax(a2)(3)f'(x)2xa1ax1ax1ax2a221(a2)(a1)a211a20,即(2a22a2a2111f(x)在,1上增,f(x)maxf(1)ln(a)1a222112只须ln(
7、a)1am(a2a3)22112(法一)设h(a)ln(a)1am(a2a3)222'12ma(4m1)a2mh(a)12ma2m1aa1'1又h(1)0h(a)在1的右侧需先增,h(1)0,m821设g(a)2ma(4m1)a2m,对称轴a114m又2m0,g(1)8m10'在(1,2)上,g(a)0,即h(a)0h(a)在(1,2)上单调递增,h(a)h(1)0112即ln(a)1am(
8、a2a3),2221于是f(x)m(a2a3)m0811ln(a)1a(法二)a22a30m222a2a311ln(a)1a设h(a)22,2a2a3a211(a2a3)ln(a)1a(2a2)'1a22h(a)22(a2a3)3aa211ln(a)22(a1)2222(a2a3)2(a1)2a3a211'(a1)(a2a3)设g(a)2