名校
解题方法
1 . 设
,
,
.
(1)求函数
,
的单调区间和极值;
(2)若关于x不等式
在区间
上恒成立,求实数a的值;
(3)若存在直线
,其与曲线
和
共有3个不同交点
,
,
(
),求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f767ccf837c2bf8019d03451849c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c2d4affa0741e2f2582dc8e957685.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1128ef28912ba41f037afea504d6bc31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ebc97d255d9f92969a741955da4ec6.png)
(2)若关于x不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a3713bb22838d9432c9e484c537e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)若存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ff39dd1dfc9caf911ad0d11ba21d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a28b3589f39573e9cc7d6684a033f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd5552324550304765749352051d850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8828dad2747f16ae4efee1ac0344a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328071ace61d03885e3bc122b2713ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830c98ceab2c157eac58caaf717b6de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
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2 . 已知函数
.
(1)讨论函数的单调性;
(2)若
有两个不同的零点
,不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254c07941a6929e0afa818a7a2176657.png)
(1)讨论函数的单调性;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2217a4ab9fc9692c87c43ed4f02a240a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec97fb7fc62f40059a13e7e69ac40e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8be675c8d80f2d734b32f929ec1493.png)
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2023-05-12更新
|
483次组卷
|
2卷引用:浙江省杭师大附2022-2023学年高二下学期期中数学试题
3 . 已知函数
.
(1)讨论
的单调性;
(2)若
恰有3个零点;
(i)求
的取值范围;
(ii)证明:在双曲线
位于第一象限内的图象上存在点
,使得对于任意实数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92882fefcdc123ac1b88f7b4722660c3.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:在双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7099d13ea829e73a848d1c7eb6570d.png)
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4 . 已知
,
为实数.
(1)若
,求
的值,并讨论
的单调性;
(2)若
时,
,求实数
的取值范围;
(3)当
时,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0be387f4ac8b5f88f2406f49f2288e.png)
,且
在
处取极值,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2080bd540326c128083efb8f1e9fc4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ea743eb9d39671af570b886b0c8149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0be387f4ac8b5f88f2406f49f2288e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf098fb6d3d4dfb8ea8dcce1bb35b496.png)
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5 . 已知函数
.
(1)若
,
,求证:
有且仅有一个零点;
(2)若对任意
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521379c626ff7729d30a8ab70c379ed0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba02974dc7ba019cc2ffad79b2a5dea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3abe34248214d7bba9ee4f4cba53d2.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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2023-05-11更新
|
1780次组卷
|
5卷引用:湖南省长沙市长郡中学、长沙一中、雅礼中学、湖南师大附中2023届高三下学期5月“一起考”数学试题
湖南省长沙市长郡中学、长沙一中、雅礼中学、湖南师大附中2023届高三下学期5月“一起考”数学试题江苏省镇江第一中学2023-2024学年高三上学期10月月考数学试题(已下线)重难点突破07 不等式恒成立问题(十大题型)-2(已下线)2024届数学新高考Ⅰ卷精准模拟(七)(已下线)黄金卷04(2024新题型)
名校
6 . 已知函数
.
(1)若对
时,
,求正实数a的最大值;
(2)证明:
;
(3)若函数
的最小值为m,试判断方程
实数根的个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfd509af00960319b088b20d3d4189a.png)
(1)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b705b0958495774d529c2e2a6c3ae94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa8a4f01a537c60d407849161a47264.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb7a27cc08a19a638e8d8a63beb4543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ce5f6bb1320b0e450042194376b25b.png)
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2023-05-08更新
|
1409次组卷
|
3卷引用:山东省实验中学2023届高三第一次模拟考试数学试题
名校
解题方法
7 . 已知函数
.
(1)若
,求
的取值范围;
(2)当
时,记函数
的两个零点为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043834eedf185e02bb0ad1bc99b7550c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3178765d82706110897df3c015378568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a851d3b31e708e63a2e3e4dc9588e236.png)
您最近一年使用:0次
2023-05-05更新
|
877次组卷
|
3卷引用:河北省名校2023届高三5月模拟数学试题
名校
8 . 已知函数
.
(1)求函数
在
处的切线方程;
(2)判断函数
在
上的单调性,并说明理由;
(3)对任意的
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef813ebc73fff5244a4f5f78e2807b18.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(3)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de3e010a4afdd8e249494099d24c2ef.png)
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2023-04-30更新
|
1093次组卷
|
3卷引用:江苏省镇江中学2023届高三下学期4月(二模)模拟数学试题
江苏省镇江中学2023届高三下学期4月(二模)模拟数学试题浙江省金华市曙光学校2023届高三三模数学试题(已下线)第九章 导数与三角函数的联袂 专题三 含三角函数的恒成立问题 微点3 三角函数的恒成立问题(三)
9 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)若函数
有两个零点
,
(其中
).
(i)求实数
的取值范围;
(ii)若存在实数
,当
时,使不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803afa3c30a4eb1a39425e44eca98cca.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0707344f1985c614bb00db33a467c9ba.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/26d8dafc71b106f39f4e15442220897b.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84ab2ea2de85f4211d3b3aaee9fc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb06adbe9ec73cfc5a0664422d41a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 已知函数
,若不等式
对
恒成立,则实数a的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b734c10d04d1129de6542284763eb6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fab10472cd59dcfe92297f3c355b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
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2023-04-26更新
|
1880次组卷
|
6卷引用:浙江省9+1高中联盟2022-2023学年高二下学期期中数学试题
浙江省9+1高中联盟2022-2023学年高二下学期期中数学试题(已下线)【2023】【高二下】【期中考】【367】【高中数学】【马定超收集】广东省广州市2023届高三冲刺(一)数学试题湖南省常德市第一中学2023-2024学年高三上学期第二次月考数学试题湖南省2024届高三数学新改革适应性训练二(九省联考题型)(已下线)专题11 不等式恒成立、能成立、恰好成立问题(过关集训)