14-15高三上·贵州遵义·阶段练习
1 . 已知函数
.
(1)若曲线
在
处的切线为
,求
的值;
(2)设![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3d3eea81768840109f218466174f7983.png)
,
,证明:当
时,
的图象始终在
的图象的下方;
(3)当
时,设
,(
为自然对数的底数),
表示
导函数,求证:对于曲线
上的不同两点
,
,
,存在唯一的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
,使直线
的斜率等于
.
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/1b4c32a0cfb14de8bc6a26a54311fedd.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6513e7d1ad16ed0ba54da88b098dc1d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3d3eea81768840109f218466174f7983.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/136995a0dea24df88860330a01092f62.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/9d2148a4da27426cbc7db6e777e7a69c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/8df1a95edcd34a89b926fc168f2aa20d.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/df61580512c44e8691de8efbd7e5053c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/fea3e068dd124c0ca98cbceba9b3347f.png)
(3)当
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/d6b34f6dada044619914cecb62849103.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/76a965da5b87446a9308156fdaaf7d8b.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3865acfd7def4e79b7d712d720b9c02c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/52b6a1f9256449b882a840dfa9462d64.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/2ec2086f962d4e64be08cb307f6d031b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5300f2d0cdf34de189a6be1b518891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631f75b2df538cc121bad64d9deb774d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/e89b836c01ae46a68c19ed11ecb9cf6e.png)
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2 . 已知函数
.
(1)讨论
的单调性;
(2)当
,
时,函数
的图象与函数
的图象有两个交点
,
.
①求证:
;
②比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5370fc919246e31862b908b13975e4f9.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881e1aef1f22f19862b3a0b09cf64efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed98e5fc99b56a2766f5c9b411253d6.png)
②比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a4f3dd93a37f788d565fc7ace0fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
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3 . 已知函数
.
(1)讨论
的单调性;
(2)若方程
有两个不相等的根
,且
的导函数为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc2a19b46639a8c5ed29281a867ba73.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e924f5b6b26534b7eea00660e9d0d9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133c30d6ca96a4d8de293da20fbe8f22.png)
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2024-02-27更新
|
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7卷引用:贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题
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4 . 已知函数
.
(1)讨论
的单调性.
(2)若有两个不相等的实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若有两个不相等的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2769ff2378bec4f25ca04fdee23d257b.png)
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解题方法
5 . 已知函数
.
(1)求证:
;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742813d9ceeb55f6fb256f064ca89cb3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5846fa96244cbf466b118d87b8c61fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知函数
,
.
(1)当
时,求证:
;
(2)若
是函数
的导函数,且
在定义域
内恒成立,求整数a的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c959ecfabe4d3d8f429f8c96467eb29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5175dc08a253b3fd0e306d015bbae502.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6292948411620a2c340542afedf898cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5465c14a0e2e8705ee70cd4e88283a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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7 . 已知函数
.
(1)当
时,证明:
只有一个零点.
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/379164b4c4bf35f19fc964dcfcb7ab02.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b581098a825ab4b15667fa1e331bc307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-12-18更新
|
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4卷引用:贵州省六盘水市2023-2024学年高三上学期第二次联考数学试题
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解题方法
8 . 已知函数
.
(1)当
时,证明:
.
(2)试问
是否为
的极值点?说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3eb38deba5a3008e2ee5026b7d2865.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99923994f2c1721fc07450b4b9656980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c5fdeae3d9934cbc3f916bd7fbf496.png)
(2)试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2024-01-09更新
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名校
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b1c0d5f732ab88f2ce487ee3285841.png)
(1)若
在
上恒成立,求a的取值范围;
(2)设
为函数g(x)的两个零点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b1c0d5f732ab88f2ce487ee3285841.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a20570016dcade92a03583ca7a74a8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6c1acba8e11c3f6474b1a998648451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c397fb14b6ebba2c4a47f96314b8334.png)
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2023-10-31更新
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10卷引用:贵州省2024届高三上学期第一次联考(月考)数学试题
贵州省2024届高三上学期第一次联考(月考)数学试题贵州省黔西南州兴义市顶效开发区顶兴学校2023-2024学年高三上学期第二次月考数学试题全国名校大联考2023-2024学年高三上学期第一联考(月考)数学试题陕西省榆林市府谷县第一中学2023-2024学年高三上学期第一次联考理科数学试题河北省保定市唐县第一中学2024届高三上学期9月月考数学试题(已下线)考点19 导数的应用--函数零点问题 2024届高考数学考点总动员【练】吉林省通榆县第一中学校2024届高三上学期第二次质量检测数学试题新疆乌鲁木齐市第七十中学2024届高三上学期第一次联考(月考)数学试题四川省2024届高三上学期第一次联考(月考)理科数学试题陕西省榆林市米脂中学2024届高三上学期第六次模拟考试数学(理)试题
解题方法
10 . 已知函数
.
(1)若
在
上单调递增,求
的取值范围;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f89f6abd0559eb5f73ea8def02c4ad3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbda14cde6775551f226484a18cdbaff.png)
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2023-10-30更新
|
452次组卷
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6卷引用:贵州省六盘水市纽绅中学等校2024届高三上学期10月联考数学试题