1 . 已知函数
.
(1)判断
的奇偶性;
(2)若
,判断
在
的单调性,并证明(定义法、导数法均可);
(3)若
,
,判断函数
的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf6edebbf204ca0e7462d7ece59fca1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/c7d013331d969749c306909529a88a49.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada9b792b1555668175c590447b02fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
名校
2 . 已知函数
,
.
(1)证明:
有唯一零点;
(2)记
的零点为
,函数
,若
在区间
有两个极值点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54892250125df38de7450de5ab41c7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffd1f6bd3686a07efa4086a02b96a9a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e95ab95ee328d5bb2579877c43b45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ad9709885514361835cb1294412896.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
(1)当
时,求函数
的值域;
(2)讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc457d4ce607a784953cbda5749766ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
4 . 已知函数
,
.
(1)求函数
的单调递增区间;
(2)若对任意
,存在
,使得
,求实数
的取值范围;
(3)若函数
,求函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fd573ad312da3c862627718e77575b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdad8acb5f4d31bfee990bf844b1a37.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e86bc8775b7d7827d7fd10a7880c46.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b55514ac04cb0b784c5e6e7d7e2f9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf4f868ee05af59275ace26167ed5bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d07623327be6016313b677059cd77d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fad5c36c01dd889f2e4a496df4d64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
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名校
5 . 已知函数
.
(1)若
时,求曲线
在点
处的切线方程;
(2)若
时,求函数
的零点个数;
(3)若对于任意
,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c716c9f6cbcba5d34b24bddc496e23.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b18ab1688df388e2df6b0aa3837741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-12-14更新
|
1318次组卷
|
6卷引用:特训03 一元函数的导数及其应用 压轴题(七大母题型归纳)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
(已下线)特训03 一元函数的导数及其应用 压轴题(七大母题型归纳)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)四川省成都市石室中学2024届高三一模数学(理)试题四川省成都市石室中学2024届高三一模数学(文)试题河北省沧州市吴桥县吴桥中学2023-2024学年高二上学期1月月考试数学试题(已下线)第3讲:利用导数研究不等式恒成立、能成立问题【练】 高三清北学霸150分晋级必备(已下线)模块三 大招14 恒成立求参——必要性探路
名校
6 . 已知函数
,若在定义域内存在
,使得
成立,则称
为函数
的“局部对称点”.
(1)若函数
在区间
内有“局部对称点”,求实数m的取值范围;
(2)若函数
在
上有“局部对称点”,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744b07c137166e10db0b54001cb93a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb12ffef15eb28fcbbd569f0676667c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828306d86dc379049e82663b7a30194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)当
时,求函数
的最小值;
(2)讨论函数
,
,
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a16d2b46560259aff4d6948b7df0184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d4d5b71587b45a3246c508b46e3221.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c7456a145f160b8266c47ea75c828c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
您最近一年使用:0次
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8 . 已知函数
,
是
的一个零点.
(1)求
的值;
(2)请把
的解析式化简成
的形式;
(3)当
时,若曲线
与直线
有2个公共点,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c2ea128fe03d542c06afec41de4b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6af3ce22c5d87280890e30afde35a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)请把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4ee9942c791efb0573c1633105fa85.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e670a46456df1a78e6f7ac39cd94fd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
您最近一年使用:0次
2023-09-10更新
|
391次组卷
|
2卷引用:北京市陈经纶中学2023-2024学年高二上学期开学检测数学试题
名校
解题方法
9 . 已知函数
是偶函数.当
时,
.
(1)若函数
在区间
上单调,求实数
的取值范围;
(2)已知
,试讨论
的零点个数,并求对应的
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829214aa98f691faf08ffe4b645f9099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5749bb82edfb623c63ae4ec6b4d43da8.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0bcc1c53e256124881a7d3d49468b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7edccedefcabf8474118ce1494310e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-09-09更新
|
419次组卷
|
4卷引用:云南省昆明市西南大学官渡实验学校2023-2024学年高二上学期9月综合素质测评数学试题
云南省昆明市西南大学官渡实验学校2023-2024学年高二上学期9月综合素质测评数学试题新疆维吾尔自治区伊犁州奎屯市第一高级中学2024届高三上学期9月月考数学试题(已下线)第四章 指数函数与对数函数 章末测试(基础)-《一隅三反》新疆维吾尔自治区伊犁州伊宁市第一中学2024届高三上学期10月月考数学试题
10 . 已知函数
,函数
在定义域内有唯一零点,且
在区间
上的最大值为16.
(1)求
的解析式;
(2)若不等式
在
上恒成立,求正整数k的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ee66360e183bbf5d55db46c02606b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ca681ae72055316ef35c01fdb27034.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33a93b07c09c346bac4c1129ea5f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b190d17d0acf5d624b034ed45059bb.png)
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