2023高三·全国·专题练习
1 . 已知
,函数
有两个零点,记为
,
.
(1)证明:
.
(2)对于
,若存在
,使得
,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77c11afffab5df60260229a316d3636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb340643ba3a6a3d0434af88044700a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc043d78e4c9ad2281754d6c1cac8791.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedf333393bdf56f8b428e9a7d2eb3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14622c24cbfdc02c762f5d7ae4ae20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267572d2dff2dc38cf9251b7f33a3e61.png)
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安徽省芜湖市第一中学2022-2023学年高三下学期4月统测数学试卷(已下线)第二篇 函数与导数专题2 中值定理 微点1 中值定理湖北省十一校2023届高三下学期第二次联考数学试题(已下线)押新高考第22题 导数综合解答题专题07导数及其应用(解答题)辽宁省大连市第二十四中学2023届高三第六次模拟考试数学试卷(已下线)模块四 专题2:导数大题分类练 (拔高卷)
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2 . 已知函数
.
(1)若
,求证:函数
在
上单调递增;
(2)若
,其中
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8b01496149bd4fcea779bf7569df4d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2a6c35384d6ebc5e47ffecb16c1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b725fdc8de9800f2692f6fea8585b1e9.png)
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3 . 设函数
,
,
.
(1)讨论
的单调性;
(2)当
且
时,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c620573e537d5f4a66f8c1b5eeb5dbd.png)
,证明:
存在极小值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f7bc44601553dd5e49f2e599579db3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0c837bc411d58b8a6663327a69fcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c620573e537d5f4a66f8c1b5eeb5dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118c9c0597d2c72126fbc4cc3927108e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4893186691de2cd41b1ecf8d079f68c9.png)
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5卷引用:安徽省芜湖市南陵中学2021-2022学年高二下学期3月第一次学情调查数学试题
安徽省芜湖市南陵中学2021-2022学年高二下学期3月第一次学情调查数学试题广东省高州市2021届高三上学期第一次模拟数学试题(已下线)名校联盟2021-2021学年高三上学期期末联考试卷理科数学试题云南省昆明市嵩明县2021-2022学年高二下学期期中考试数学试题辽宁省朝阳市北票市高级中学2022-2023学年高二下学期期中数学试题
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4 . 已知
,函数
.
(1)若函数
在
上单调递增,求a的取值范围;
(2)用反证法证明:函数
不可能为
上的单调函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599e8b50f93c5f838e1f90472f04d032.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84d41b94678bd8e3c114f40adb5425c.png)
(2)用反证法证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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5 . 已知函数
.
(1)若
存在极值,求实数a的取值范围;
(2)设
,设
是定义在
上的函数.
(ⅰ)证明:
在
上为单调递增函数(
是
的导函数);
(ⅱ)讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b75797c53c96bf418ef9811eb10c16e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46b4c7585238f53d85f5a96d35d95af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c3e0694b3cf627d03350a94a018764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e2ab9827878644d41cca5ad99c17f0.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f539a9f59662e4a7be3e758fd603d1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e2ab9827878644d41cca5ad99c17f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(ⅱ)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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2020-05-26更新
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2014·安徽芜湖·二模
解题方法
6 . 已知函数
,
,对于任意的
,都有
.
(1)求
的取值范围
(2)若
,证明:
(
)
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71abc90faff792b91b6a5d878b7e8f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6aa8089b5d9b722aff679af3c4d289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1254070260067f8bf2fec39a7d0c8f1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e94a992b87d25da74d10302af39a06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142184c158dcda3e8aa9aa2a47d28872.png)
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcb245c0c4c4b230b5f33ccbe192aec.png)
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