名校
1 .
,
,则
最小值为______ .若
与
无交点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6989cc6bc212764fc7c1dfe45d57bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24d7a51950ec8ef70c8db2b5b6fa794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 若
,设
的零点分别为
,
,…,
,则n=_______________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907f92dfdd6bbe696b695cf471c68f1e.png)
_______________ .(其中
为a向上取整,例如:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f1bbc0d46686c6ca96cf2246c8c2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907f92dfdd6bbe696b695cf471c68f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0306c8a9b082d56b04c967093ddf256a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac34cb60f3741fe82af6767a7df7b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcc93b32bccf6f1331a499168391bea.png)
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2023年新老高考过渡省份适应性联考数学试题新疆乌鲁木齐市兵团二中2024届高三上学期第四次月考数学试题(已下线)第五章 一元函数的导数及其应用(压轴题专练,精选34题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)
2023·江西·二模
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3 . 若
,设
的零点分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907f92dfdd6bbe696b695cf471c68f1e.png)
___________ .(其中
表示a的整数部分,例如:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dbbbb107c1df5cf5227c081169e6f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907f92dfdd6bbe696b695cf471c68f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc520cc41fdb61f9e3bd5d7c0baa1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d67e676a12362f0906d5ff551cc918.png)
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7卷引用:江西省名校协作体联盟2023届高三第二次联考模拟考试数学(理)试题
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解题方法
4 . 已知函数
恰有两个零点
,
和一个极大值点
,且
,
,
成等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b029ff1ec707abd0d2a14b9a3d4c2082.png)
__________ ;若
的解集为
,则
的极大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b269dce1ae3396d2afc82a91dc6f97ba.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/90aa505e4e41dd4becc7e55d2e938f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b029ff1ec707abd0d2a14b9a3d4c2082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85db4f72795b4a150a734d835ffbd913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c253ea436c94f88bd5a3ddb799ef30ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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5卷引用:2023年普通高等学校招生星云线上统一模拟考试Ⅰ数学试卷
5 . 已知函数
有两个零点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
________
(填大于或小于号),实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b526c857bb86d48793b88199a32ecb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 已知函数
(
),若函数
的极值为0,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ ;若函数
有且仅有四个不同的零点,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f3ad70b1a7861dd1d0325d3b808a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed4f8de915199a8b08ea2d67eef36e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知函数
,则函数
的最小值为___________ ;若关于x的方程
有且仅有一个实根,则实数a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec2c8e9393ba912b68d1b72f64ca9cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa48a5a96ea5b1a51d99cf233937a68.png)
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山东省济南市2022届高三二模数学试题福建省厦门第一中学2021-2022学年高二6月适应性练习数学试题(已下线)山东省济南市2022届高三二模数学试题变式题11-16(已下线)第五章 一元函数的导数及其应用(压轴题专练,精选34题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)(已下线)专题12 导数的综合问题(过关集训)
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8 . 已知函数
(
,e为自然对数的底数,e =2.71828…).当a=1时,函数
在点P(1,
)处的切线方程为________ ;若
,
,则实数a的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914eaf8335244d9a56f95053c79ce9d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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9 . 已知函数
.当
时,不等式
的解集是___________ ;若
是
的极值点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5e9a0f3b8d7c8e9b935e6699db8aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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10 . 已知函数
,若存在实数
使得
,则
的取值范围是___________ ;若
,则
的最大值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae53a7bac4c0efc58f49ce8963d2033d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581e1fd6cef0f01367251c3f323085b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e8b230513c1934f2c29bb19b54d4c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfa99136d0bb3533d85d1cb9a308ad4.png)
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4卷引用:黑龙江省哈尔滨市第三中学2021-2022学年高三第四次验收考试数学(理科)试题
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