名校
1 . 已知
是方程
的两个实根,且
.
(1)求实数
的取值范围;
(2)已知
,
,若存在正实数
,使得
成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37674da31fc7bffe11c6b45f52cd2bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e9ecfdf2ec90ea96e104158aec81c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3f8115a9459a4a386008c2b8d56de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd5b2efe2aafa920ecb259f276e2d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4d89f6c10871a7b3475c00801f608d.png)
您最近一年使用:0次
2023-05-26更新
|
1403次组卷
|
6卷引用:浙江省杭州第二中学等四校2023届高三下学期5月高考模拟数学试题
浙江省杭州第二中学等四校2023届高三下学期5月高考模拟数学试题 湖南省长沙市第一中学2022-2023学年高二下学期第三次阶段性测试数学试题重庆市万州第二高级中学2024届高三上学期8月月考数学试题(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)2023届浙江省四校联盟高三下学期数学模拟试卷(已下线)专题19 导数综合-2
名校
2 . 已知:函数
,且
,
.
(1)求证:
;
(2)设
,试比较
,
,
,
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5908da764a876b13a321d5317388f00.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f9d3e45494d3d5ac3bc405f7c7cb30.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada5e0f6acc0871207e3e4f28988b129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636e33ba3b8274ffaaef658142e83a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cb7812970c2f83eee4582761df5caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75bc9338a97791e4c6cfd21b57091e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b3de8b9a803f3b669023cb47b573aa.png)
您最近一年使用:0次
2023-05-20更新
|
1142次组卷
|
6卷引用:广东实验中学2024届高三上学期第一次阶段考试数学试题
广东实验中学2024届高三上学期第一次阶段考试数学试题(已下线)广东实验中学2024届高三上学期第一次阶段考试数学试题变式题19-22湖北省孝感、荆州部分中学2022-2023年高三下学期5月联考数学试题湖北省襄阳市第四中学2023届高三下学期5月适应性考试(三)数学试题(已下线)专题05 导数大题(已下线)专题07 函数与导数常考压轴解答题(练习)
名校
3 . 已知
与
有相同的最小值.
(1)求实数
的值;
(2)已知
,函数
有两个零点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b4508603624f22ec78a62e2c845ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b861ae69918c1e73a725e98f474825.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26051acb6dd6e8272071781084d0b1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75dc84060c6520c53cbc2510b801976a.png)
您最近一年使用:0次
2023-05-13更新
|
867次组卷
|
2卷引用:东北三省四市教研联合体2023届高三二模数学试题
名校
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)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
是
的导函数.
(1)求函数
的极值;
(2)若函数
有两个不同的零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de619d3a8a2f9ee2da3cc43280971670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
(2)若函数
![](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/08cf1d9986814081600cee9a19a24860.png)
您最近一年使用:0次
2023-05-08更新
|
853次组卷
|
4卷引用:模块六 专题12 易错题目重组卷(云南卷)
(已下线)模块六 专题12 易错题目重组卷(云南卷)四川省内江市威远中学2022-2023学年高二下学期第二次阶段性考试数学(理)试题云南省曲靖市2023届高三第二次教学质量监测数学试题(已下线)专题19 导数综合-1
2023·全国·模拟预测
解题方法
6 . 已知函数
,
.
(1)讨论
的极值;
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e195befea2d63147348a09d60eb3e6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff845a3ad36c0fa30fa57254b12d8d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4fa244744c7bc9b391e5c2f8fb6475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa7a5599024602e3d378cbf65722202.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)若
在
单调递增,求实数
的取值范围;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e5525f126f26e9f8b8b53e0a03951.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f909328384f9c52134243753d9c954ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a6441e45f5fbd82ba8f26c905645b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edacb490a7367b0a82edd39caa1439bd.png)
您最近一年使用:0次
8 . 已知函数
.
(1)讨论函数
在
上的零点个数;
(2)当
且
时,记
,探究
与1的大小关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81eeb610596766eb3d36bf33f603953.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499a8449e8bb253065463c23f3ff5860.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff537b9287dffb28e89bfc2bf5ed723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2a14d9c7f3d948525c2660db272223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.png)
您最近一年使用:0次
2023-05-02更新
|
709次组卷
|
6卷引用:山西省运城市2023届高三三模数学试题(A卷)
名校
解题方法
9 . 曲线的曲率是针对曲线上某个点的切线方向角对弧长的转动率,曲线的曲率越大,表示曲线的弯曲程度越大,若记
,则函数
在点
处的曲率为
.
(1)求证:抛物线
(
)在
处弯曲程度最大;
(2)已知函数
,
,
,若
,
曲率为0时
的最小值分别为
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122ee49e92147a80e2316e77f69284ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01a4e711e604b12fb6ffaa5ac773f07.png)
(1)求证:抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432b2ea4adca1484f86c8935d76b4fba.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c0ec3dd39151bef6391c47d9815a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c2f0ada24ff024834f831aa3bc2bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/9f3966bd8e4857ccb70afc0fdbab8e87.png)
您最近一年使用:0次
2023-05-01更新
|
1323次组卷
|
4卷引用:湖南省长沙市长郡中学、河南省郑州外国语学校 、浙江省杭州第二中学2023届高三二模联考数学试题
湖南省长沙市长郡中学、河南省郑州外国语学校 、浙江省杭州第二中学2023届高三二模联考数学试题黑龙江省哈尔滨市第九中学校2023届高三第四次模拟数学试题(已下线)第五篇 向量与几何 专题21 曲率与曲率圆 微点2 曲率与曲率圆(二)(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)
解题方法
10 . 已知函数
,
.
(1)若
是R上的减函数,求实数a的取值范围;
(2)若
有两个极值点
,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81cbbc9c0e660de74ec1e166c2b81b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4173ff3adec126f18463e008a3234597.png)
您最近一年使用:0次
2023-04-29更新
|
853次组卷
|
3卷引用:江西省上饶市2023届高三二模数学(理)试题