名校
1 . 设
且
恒成立.
(1)求实数
的值;
(2)证明:
存在唯一的极大值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca551efa0de79e19f32192114f70499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](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/99bf35ae2933898fb81a768a114ade4d.png)
您最近一年使用:0次
2 . 已知函数
.
(1)讨论函数
的单调性;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1acabec979fb2ef1791226dfe415a88.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01afae1df9d93011c1e4805d29d07bf5.png)
您最近一年使用:0次
解题方法
3 . 已知函数
的最小值为
.
(1)求实数
的值;
(2)若
有两个不同的实数根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49640d356411eb3e1d51f68deddbe469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88cfacc95887672ab01766ea5a703332.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)当
时,探究
零点的个数;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a8626ddaa97c93992880572317341b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d4b7ca6b8f3ac9952f5683e5f15076.png)
您最近一年使用:0次
2024-02-04更新
|
864次组卷
|
3卷引用:安徽省合肥一六八中学等学校2024届高三上学期名校期末联合测试数学试题
名校
解题方法
5 . 已知函数
,
.
(1)当
时,求曲线
在
处的切线方程;
(2)求
的单调区间;
(3)设
是函数
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1237be7b7b3712cfe108061534ef7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](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/5828873f8369183faf71181cda5b61d2.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aabc96b7433bba077ceac76d8f0d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00210f79b04a8f6bc1922433d00bc89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ac3f646599fe63ff886d34750e4e6a.png)
您最近一年使用:0次
2024-01-25更新
|
1823次组卷
|
5卷引用:天津市宁河区2024届高三上学期期末数学试题
天津市宁河区2024届高三上学期期末数学试题福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题(已下线)重难点2-4 利用导数研究不等式与极值点偏移(8题型+满分技巧+限时检测)(已下线)2023-2024学年高二下学期第一次月考解答题压轴题十六大题型专练(2)(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练
解题方法
6 . 已知函数
,
为实数.
(1)若
在
上单调递增,求实数
的取值范围;
(2)若
.
①证明:
既有极大值又有极小值;
②若
,
分别为函数
的极大值和极小值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363aaad7b209645176bb88f91765218b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113cd76ec8016056cda65fea47359299.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a23d05ff2aee22d9da978f30ff84ca0.png)
您最近一年使用:0次
7 . 已知函数
与
的图象关于直线
对称,若
,构造函数
.
(1)当
时,求函数
在点
处的切线与坐标轴围成三角形的面积;
(2)若
(其中
为
的导函数),当
时,
,证明:
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca5c70f5cb1caf91827aa7d3041f37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a3f617721f69da3649d17ec9c59602.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c97d54952104950bfd7afc0176bbd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339416541b598f3c1fd390ef1b3251b3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752bf766bc202c8cb83e4c6a9abe989f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424ef928fdc9de964b00ad253701959e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fed1a157dd189c3a1f20868a121cad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07d4b1e7127c7eb1fb914837256d70.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
,
.
(1)若对于任意
,都有
,求实数
的取值范围;
(2)若函数
有两个零点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19235af93513ae52117810409db6b8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d6cf10c27ff8eb7f23f40a8f4b1381.png)
(1)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e312eca38032174f9739126b81d012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ea94f11a28aceb8ac7a7be2080f135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c534f574156e120f4a8d9ebef47ede.png)
您最近一年使用:0次
9 . 已知函数
的导函数为
.
(1)若
,求曲线
在点
处的切线方程.
(2)若
存在两个不同的零点
,
(ⅰ)求实数
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e15ecb3e777a4767f56bb7ceb105d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c701c5c07f7c584aadd218d9e341d3ac.png)
您最近一年使用:0次
解题方法
10 . (1)求函数的极值;
(2)若,证明:当
时,
.
您最近一年使用:0次
2024-02-14更新
|
848次组卷
|
5卷引用:河南省焦作市2024届高三一模数学试题
河南省焦作市2024届高三一模数学试题河南省安阳市2024届高三第一次模拟考试数学试卷(已下线)重难点2-5 利用导数研究零点与隐零点(7题型+满分技巧+限时检测)天一大联考2024届高三毕业班阶段性测试(五) 数学试题陕西省安康市高新中学2023-2024学年高三下学期2月月考理科数学试题