(完整word版)高中数学导数的应用——极值与最值专项训练题(全).pdf

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(完整word版)高中数学导数的应用——极值与最值专项训练题(全).pdf

高中数学专题训练导数的应用极值与最值一、选择题1函数 yax3bx2取得极大值和极小值时的x 的值分别为 0 和13，则()Aa2b0B2ab0 C2ab0 Da2b0 答案D 解析y3ax22bx，据题意，0、13是方程 3ax22bx0 的两根2b3a13，a2b0.2当函数 yx 2x取极小值时，x()A.1ln2B1ln2Cln2 Dln2 答案B 解析由 yx 2x得 y2xx 2x ln2 令 y0 得 2x(1x ln2)0 2x0，x1ln23函数 f(x)x33bx3b 在(0,1)内有极小值，则()A0b1 Bb1 Cb0 Db12答案A 解析f(x)在(0,1)内有极小值，则 f(x)3x23b 在(0,1)上先负后正，f(0)3b0，b0，f(1)33b0，b1 综上，b 的范围为 0b1 4连续函数f(x)的导函数为f(x)，若(x1)f(x)0，则下列结论中正确的是()Ax1 一定是函数 f(x)的极大值点Bx1 一定是函数 f(x)的极小值点Cx1 不是函数 f(x)的极值点Dx1 不一定是函数 f(x)的极值点答案B 解析x1时，f(x)0 x1 时，f(x)0 连续函数 f(x)在(，1)单减，在(1，)单增，x1 为极小值点5函数 yx33x23x4 在0,2上的最小值是()A173B103C4 D643答案A 解析yx22x3.令 yx22x30，x3 或 x1 为极值点当 x0,1时，y0，所以当 x1 时，函数取得极小值，也为最小值当x1 时，ymin173.6函数 f(x)的导函数 f(x)的图象，如右图所示，则()Ax1 是最小值点Bx0 是极小值点Cx2 是极小值点D函数 f(x)在(1,2)上单增答案C 解析由导数图象可知，x0，x2 为两极值点，x0 为极大值点，x2为极小值点，选 C.7已知函数 f(x)12x3x272x，则 f(a2)与 f(1)的大小关系为()Af(a2)f(1)Bf(a2)f(1)Cf(a2)f(1)Df(a2)与 f(1)的大小关系不确定答案A 解析由题意可得 f(x)32x22x72.由 f(x)12(3x7)(x1)0，得 x1 或 x73.当 x1 时，f(x)为增函数；当 1x12时，f(x)0；当 x0.x12时取极大值，f(12)1e1212e.二、填空题9若 yalnxbx2x 在 x1 和 x2 处有极值，则a_，b_.答案2316解析yax2bx1.由已知a2b10a24b10，解得a23b1610已知函数 f(x)13x3bx2c(b，c 为常数)当 x2 时，函数 f(x)取得极值，若函数 f(x)只有三个零点，则实数c 的取值范围为 _ 答案0c0f 2 132322c0，解得 0c43文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R211设 mR，若函数 yex2mx(xR)有大于零的极值点，则m 的取值范围是_答案m1，即 m0，所以不存在实数 a，使得 f(x)是(，)上的单调函数15已知定义在 R 上的函数 f(x)x2(ax3)，其中 a 为常数(1)若 x1 是函数 f(x)的一个极值点，求a 的值；(2)若函数 f(x)在区间(1,0)上是增函数，求 a 的取值范围解析(1)f(x)ax33x2，f(x)3ax26x3x(ax2)x1 是 f(x)的一个极值点，f(1)0，a2.(2)解法一当 a0 时，f(x)3x2在区间(1,0)上是增函数，a0 符合题意；当 a0 时，f(x)3ax(x2a)，令 f(x)0 得：x10，x22a.当 a0 时，对任意 x(1,0)，f(x)0，a0 符合题意；当 a0，2a1，2a0 符合题意；综上所述，a2.解法二f(x)3ax26x0 在区间(1,0)上恒成立，3ax60，a2x在区间(1,0)上恒成立，又2x212，a2.16已知函数 f(x)x2ax1lnx.(1)若 f(x)在(0，12)上是减函数，求 a 的取值范围；(2)函数 f(x)是否既有极大值又有极小值？若存在，求出a 的取值范围；若不存在，请说明理由解析(1)f(x)2xa1x，f(x)在(0，12)上为减函数，x(0，12)时2xa1x0 恒成立，即 a4，g(x)g(12)3，a3.(2)若 f(x)既有极大值又有极小值，则f(x)0 必须有两个不等的正实数根x1，x2，即 2x2ax10 有两个不等的正实数根故 a 应满足 0a20?a280a0?a2 2，当a22时，文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2f(x)0 有两个不等的实数根，不妨设 x1x2，由 f(x)1x(2x2ax1)2x(xx1)(xx2)知，0 xx1时 f(x)0，x1x0，xx2时 f(x)2 2时 f(x)既有极大值 f(x2)又有极小值 f(x1)1.已知 yf(x)是奇函数，当x(0,2)时，f(x)lnxax(a12)，当 x(2,0)时，f(x)的最小值为1，则 a 的值等于 _答案1 解析 f(x)是奇函数，f(x)在(0,2)上的最大值为 1，当 x(0,2)时，f(x)1xa，令 f(x)0 得 x1a，又 a12，01a0，则 x1a，f(x)在(0，1a)上递增；令 f(x)1a，f(x)在(1a，2)上递减，f(x)maxf(1a)ln1aa1a1，ln1a0，得 a1.2设函数 f(x)2x33ax23bx8c 在 x1 及 x2 时取得极值(1)求 a、b 的值；(2)若对任意的 x0,3，都有 f(x)0；当 x(1,2)时，f(x)0.所以，当 x1 时，f(x)取得极大值 f(1)58c.又 f(0)8c，f(3)98c，则当 x0,3时，f(x)的最大值为 f(3)98c.因为对于任意的 x0,3，有 f(x)c2恒成立，所以 98cc2，解得 c9.文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2因此 c 的取值范围为(，1)(9，)3已知函数 f(x)x33ax23x1.(1)设 a2，求 f(x)的单调区间；(2)设 f(x)在区间(2,3)中至少有一个极值点，求a 的取值范围解析(1)当 a2 时，f(x)x36x23x1，f(x)3(x23)(x23)当 x(，23)时 f(x)0，f(x)在(，2 3)上单调增加；当 x(23，23)时 f(x)0，f(x)在(23，23)上单调减少；当 x(23，)时 f(x)0，f(x)在(23，)上单调增加综上，f(x)的单调增区间是(，23)和(23，)，f(x)的单调减区间是(23，23)(2)f(x)3(xa)21a2当 1a20 时，f(x)0，f(x)为增函数，故 f(x)无极值点；当 1a20 时，f(x)0 有两个根，x1aa21，x2aa21.由题意知，2aa213，或 2aa213.式无解式的解为54a53.因此 a 的取值范围是(54，53)1“我们称使 f(x)0 的 x 为函数 yf(x)的零点若函数yf(x)在区间 a，b上是连续的，单调的函数，且满足f(a)f(b)0，f(x)在2,7上单调递减，又 f(7)6ln83618(ln22)0，文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2 f(2)f(7)0.f(x)在2,7上有唯一零点当 x7，)时，f(x)f(7)0)(1)当 a1 时，求 f(x)的单调区间；(2)若 f(x)在(0,1上的最大值为12，求 a 的值解析函数 f(x)的定义域为(0,2)，f(x)1x12xa.(1)当 a1 时，f(x)x22x 2x，所以 f(x)的单调递增区间为(0，2)，单调递减区间为(2，2)；(2)当 x(0,1时，f(x)22xx 2xa0，即 f(x)在(0,1上单调递增，故f(x)在(0,1上的最大值为 f(1)a，因此 a12.3已知函数 f(x)x33x29xa.(1)求 f(x)的单调递减区间；(2)若 f(x)在区间 2,2上的最大值为 20，求它在该区间上的最小值分析本题考查多项式的导数公式及运用导数求函数的单调区间和函数的最值，题目中需注意应先比较f(2)和 f(2)的大小，然后判定哪个是最大值从而求出 a.解(1)f(x)3x26x9.令 f(x)0，解得 x3，函数f(x)的单调递减区间为(，1)，(3，)(2)f(2)81218a2a，f(2)81218a22a，f(2)f(2)在(1,3)上 f(x)0，f(x)在(1,2上单调递增又由于 f(x)在2，1)上单调递减，f(1)是 f(x)的极小值，且 f(1)a5.文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2 f(2)和 f(1)分别是 f(x)在区间 2,2上的最大值和最小值，于是有22a20，解得 a2.f(x)x33x29x2.f(1)a57，即函数 f(x)在区间 2,2上的最小值为 7.4已知函数 f(x)xex(xR)(1)求函数 f(x)的单调区间和极值；(2)已知函数 yg(x)的图象与函数 yf(x)的图象关于直线 x1 对称证明当x1 时，f(x)g(x)；(3)如果 x1x2，且 f(x1)f(x2)，证明 x1x22.解析(1)f(x)(1x)ex.令 f(x)0，解得 x1.当 x变化时，f(x)，f(x)的变化情况如下表：x(，1)1(1，)f(x)0f(x)极大值所以 f(x)在(，1)内是增函数，在(1，)内是减函数函数 f(x)在 x1 处取得极大值 f(1)，且 f(1)1e.(2)由题意可知 g(x)f(2x)，得 g(x)(2x)ex2.令 F(x)f(x)g(x)，即 F(x)xex(x2)ex2，于是 F(x)(x1)(e2x21)ex.当 x1 时，2x20，从而 e2x210，又 ex0.所以 F(x)0.从而函数 F(x)在1，)上是增函数又 F(1)e1e10，所以 x1 时，有 F(x)F(1)0，即 f(x)g(x)(3)若(x11)(x21)0，由(1)及 f(x1)f(x2)，得 x1x21，与 x1x2矛盾若(x11)(x21)0，由(1)及 f(x1)f(x2)，得 x1x2，与 x1x2矛盾根据得(x11)(x21)0，不妨设 x11，x21.由(2)可知，f(x2)g(x2)，g(x2)f(2x2)，所以 f(x2)f(2x2)，从而 f(x1)f(2x2)，因为 x21，所以 2x21，又由(1)可知函数 f(x)在区间(，1)内是增函数，所以 x12x2，即 x1x22.5已知函数 f(x)ax332ax2，函数 g(x)3(x1)2.(1)当 a0时，求 f(x)和 g(x)的公共单调区间；(2)当 a2时，求函数 h(x)f(x)g(x)的极小值；(3)讨论方程 f(x)g(x)的解的个数解(1)f(x)3ax23ax3ax(x1)，又 a0，由 f(x)0 得 x1，文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R7R2文档编码:CB7D7U1F6K1 HL6V9B3R10I10 ZO6D8O2R

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