名校
1 . 已知
.
(1)求函数
的单调区间和极值;
(2)请严格证明曲线
有唯一交点;
(3)对于常数
,若直线
和曲线
共有三个不同交点
,其中
,求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647014ad8af603468f4100043c4bde15.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(2)请严格证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(3)对于常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059524807d8e93433b8d994df6ede70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
您最近一年使用:0次
2023-12-19更新
|
636次组卷
|
3卷引用:专题09 导数(三大类型题)15区新题速递
2 . 已知
,
(1)求函数
的导数,并证明:函数
在
上是严格减函数(常数
为自然对数的底);
(2)根据(1),判断并证明
与
的大小关系,并请推广至一般的结论(无须证明);
(3)已知
、
是正整数,
,
,求证:
是满足条件的唯一一组值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b4888d8cf85f200763db925ce501b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(2)根据(1),判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8520e118f7e2aab0cea0fc23c833ccbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15d2a3cd491be27bc3d8799b3f9f610.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdc0e0ca559f0f1af6127545f356fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e1c681b27df538bd4742f6cd8298ae.png)
您最近一年使用:0次
2022-12-15更新
|
808次组卷
|
5卷引用:核心考点09导数的应用(1)
(已下线)核心考点09导数的应用(1)上海市嘉定区2023届高三上学期一模数学试题上海市静安区市北中学2024届高三上学期12月月考数学试题(已下线)上海市高二下学期期末真题必刷01(易错题)--高二期末考点大串讲(沪教版2020选修)重庆市2023届高三下学期2月月度质量检测数学试题
名校
解题方法
3 . 在平面直角坐标系
中,对于直线
和点
、
,记
,若
,则称点
、
被直线
分隔,若曲线
与直线
没有公共点,且曲线
上存在点
、
被直线
分隔,则称直线
为曲线
的一条分隔线.
(1)判断点
是否被直线
分隔并证明;
(2)若直线
是曲线
的分隔线,求实数
的取值范围;
(3)动点
到点
的距离与到
轴的距离之积为
,设点
的轨迹为曲线
,求证:通过原点的直线中,有且仅有一条直线是
的分隔线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fa0e0526598c4140789f6328daac9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653fe002a6d9968d6b1d2e7ec36d178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4869bf9983f59598ca7954fd7e89b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b3d5b330a1e9746267f1a80482e435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a93e8201cd8010f841a105bc9afd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76e726cd6ff947e0ae20c07ebfa8bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348aca26e61218d251581e21c1129a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378e03d75c73c8ca71f991a8c07729a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
解题方法
4 . 已知双曲线
,经过点
的直线
与该双曲线交于
两点.
(1)若
与
轴垂直,且
,求
的值;
(2)若
,且
的横坐标之和为
,证明:
.
(3)设直线
与
轴交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e250158df0fcb0b51013bd626545e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac8fa800c00933279f2b20e5034438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138c0f0b71a955d0a4f249d57b53d5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a563c50a7f6d10fa46339d7107fc85e.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb6ee119dc122c6bda124041812a2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
2020-05-20更新
|
508次组卷
|
5卷引用:热点04 平面向量、复数-2021年高考数学【热点·重点·难点】专练(上海专用)
(已下线)热点04 平面向量、复数-2021年高考数学【热点·重点·难点】专练(上海专用)2020届上海杨浦区高三二模数学试题上海市致远高中2020-2021学年高二上学期12月月考数学试题上海市同济大学第二附属中学2024届高三上学期期中数学试题西藏拉萨市部分学校2023-2024学年高二上学期期末模拟数学试题(理科)
名校
5 . 如图,已知曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8664e94c5793590f8d478e20908317c6.png)
,曲线
,P是平面上一点,若存在过点P的直线与
都有公共点,则称P为“
型点”.
![](https://img.xkw.com/dksih/QBM/2020/1/9/2373535080144896/2373593427968000/STEM/e4434afaff9a491eb01394e08d051e00.png?resizew=173)
(1)若
,
时,判断
的左焦点
是否为“
型点”,并说明理由;
(2)设直线
与
有公共点,求证
,进而证明原点不是“
型点”;
(3)若圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.png)
内的任意一点都不是“
型点”,试写出a、b满足的关系式,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8664e94c5793590f8d478e20908317c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4b0a3b2e59998deacae94069bcc5ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f844bab7df19b7dc383019f5fb34e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
![](https://img.xkw.com/dksih/QBM/2020/1/9/2373535080144896/2373593427968000/STEM/e4434afaff9a491eb01394e08d051e00.png?resizew=173)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadd2e6f0aa16c2c466c904474ffc79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553288bc51ba6174dab2e0175d2df90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
(3)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9314b34791285525ebef09afa9d2b922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
您最近一年使用:0次
名校
6 . 给出集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c0d57080c83dfae371038b34fbc57.png)
(1)若
求证:函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d4f7bcbafb423271f97e0d407c74ec.png)
(2)由(1)可知,
是周期函数且是奇函数,于是张三同学得出两个命题:
命题甲:集合M中的元素都是周期函数;命题乙:集合M中的元素都是奇函数,请对此给出判断,如果正确,请证明;如果不正确,请举出反例;
(3)设
为常数,且
求
的充要条件并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c0d57080c83dfae371038b34fbc57.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca64afa00211df204a6302463890edbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d4f7bcbafb423271f97e0d407c74ec.png)
(2)由(1)可知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d95da33526f7713ce2016bfa6efe0f.png)
命题甲:集合M中的元素都是周期函数;命题乙:集合M中的元素都是奇函数,请对此给出判断,如果正确,请证明;如果不正确,请举出反例;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99ac91fc1e9097126e4c2aa20cdeffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc1d1fd01b97f1f5414428bc0d711d0.png)
您最近一年使用:0次
名校
7 . 已知椭圆:
的左右焦点为
、
,左右顶点分别为
、
,
是椭圆上异于
、
的点.
(1)求
的周长;
(2)若过
的直线
与椭圆交于
、
两点,且
,求
的值;
(3)若直线
过点
且与
轴垂直,直线
交直线
于点
,判断以
为直径的圆与直线
的位置关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95972549c82ba198e8b7382fc72882e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
您最近一年使用:0次
名校
8 . 已知
,
,
是自然对数的底数.
(1)当
时,求函数
的极值;
(2)若关于
的方程
有两个不等实根,求
的取值范围;
(3)当
时,若满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20a21999ea818acdfb48d3641f70d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0369099d128586f54e7d566a5cdc5686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdc729607cf42c430488ff4bd2cd4f2.png)
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3卷引用:专题05导数及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)
真题
9 . 对于一个函数
和一个点
,令
,若
是
取到最小值的点,则称
是
在
的“最近点”.
(1)对于
,求证:对于点
,存在点
,使得点
是
在
的“最近点”;
(2)对于
,请判断是否存在一个点
,它是
在
的“最近点”,且直线
与
在点
处的切线垂直;
(3)已知
在定义域R上存在导函数
,且函数
在定义域R上恒正,设点
,
.若对任意的
,存在点
同时是
在
的“最近点”,试判断
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e75192ed6ee73f295754edfbbb4a4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be20e3724274132cb83b16deaeecfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6085b118b86f7f4dd54864e113cd595c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7bce420cf236e5f429afee284239010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3641338ac7fd85ef574690ba1f988d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6be4ab05ff885a4a6a043eaebe7a91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf6463a6ee745687de1ee10f4d40253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90183525765a8279328417af4bf6179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237c115d5b39d761e1cbcae031070b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
10 . 已知常数
,设
,
(1)若
,求函数
的最小值;
(2)是否存在
,且
,
,
依次成等比数列,使得
、
、
依次成等差数列?请说明理由.
(3)求证:“
”是“对任意
,
,都有
”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df71f8b32945f3915dd2a0b72593bed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1757236a5ef1fc70a18f31d6d2438b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9769116ec47353514e6b7fb7b17216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542893790445d6d888d9ff91fd215c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1e5fb2d54a62f243bd5936a3f60386.png)
(3)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a878fd5a7104a7f42770a19097d56457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a620b284ae80049376c7a7c9afab1f62.png)
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