14-15高三上·贵州遵义·阶段练习
1 . 已知函数
.
(1)若曲线
在
处的切线为
,求
的值;
(2)设![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3d3eea81768840109f218466174f7983.png)
,
,证明:当
时,
的图象始终在
的图象的下方;
(3)当
时,设
,(
为自然对数的底数),
表示
导函数,求证:对于曲线
上的不同两点
,
,
,存在唯一的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
,使直线
的斜率等于
.
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/1b4c32a0cfb14de8bc6a26a54311fedd.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6513e7d1ad16ed0ba54da88b098dc1d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3d3eea81768840109f218466174f7983.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/136995a0dea24df88860330a01092f62.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/9d2148a4da27426cbc7db6e777e7a69c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/8df1a95edcd34a89b926fc168f2aa20d.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/df61580512c44e8691de8efbd7e5053c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/fea3e068dd124c0ca98cbceba9b3347f.png)
(3)当
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/d6b34f6dada044619914cecb62849103.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/76a965da5b87446a9308156fdaaf7d8b.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3865acfd7def4e79b7d712d720b9c02c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/52b6a1f9256449b882a840dfa9462d64.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/2ec2086f962d4e64be08cb307f6d031b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5300f2d0cdf34de189a6be1b518891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631f75b2df538cc121bad64d9deb774d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/e89b836c01ae46a68c19ed11ecb9cf6e.png)
您最近一年使用:0次
解题方法
2 . 已知函数
,函数
的单调递减区间为
,且函数
的极小值为0.
(1)求函数
的解析式;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae06c488100e31570805778b1d322e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42905b1f3b6415509e354731a671970a.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)求曲线
在点
处的切线方程,
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903f1f0c9ff9bc834d16dfed6359f411.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c069903b3b06877ffa9d6db7fbc5c57.png)
您最近一年使用:0次
2023-12-19更新
|
1846次组卷
|
12卷引用:贵州省遵义市2024届高三上学期12月月考数学试题
贵州省遵义市2024届高三上学期12月月考数学试题湖北省部分学校2024届高三上学期12月联考数学试题陕西省商洛市2024届高三一模数学(文)试题海南省2024届高三上学期一轮复习调研考试(12月联考)数学试题陕西省商洛市2024届高三一模数学(理)试题福建省部分学校2024届高三上学期12月月考数学试题山东省潍坊市昌乐第一中学2024届高三上学期12月月考数学试题(已下线)专题2-6 导数大题证明不等式归类-3河南省三门峡市2024届高三上学期第一次大练习数学试题(已下线)模块四 第五讲:利用导数证明不等式【练】广东省中山市桂山中学2023-2024学年高二下学期第一次段考检测数学试题陕西省西安市长安区第一中学2023-2024学年高二下学期期中考试数学试题
解题方法
4 . 设函数
.
(1)若函数
在定义域内单调递增,求
的取值范围;
(2)若不等式
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b81201c3429d401ff1e14d34eb94075.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f0c35ddcf222558b2a6d1546128825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5354b073a1f30b5be23e4910613652.png)
您最近一年使用:0次
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c45d730f7de4d2534217e165831454.png)
(1)求
的极值;
(2)当
,
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c45d730f7de4d2534217e165831454.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef6a9bc8be0f6d89596d91f8c2b3dd8.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
.
(1)求函数
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed74d3f0565cf8ac4e2ce48ce77cb3c7.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3bfdb715c6eb7d85aeae75a4afe9d26.png)
您最近一年使用:0次
名校
7 . 已知
.
(1)求函数
的单调区间;
(2)若函数
有两个零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786999ff39b91fac93044fb70679be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112293429caa01e7670ebcaf5bf95de.png)
您最近一年使用:0次
2022-08-22更新
|
212次组卷
|
2卷引用:贵州省遵义市新高考协作体2023届高三上学期入学质量监测数学(文)试题
8 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)若
,
,
,请比较a,b,c的大小;
(2)若函数
有两个零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ccdf28e62c595d1f0337b18d70266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba48368ed6dd4b0f6d49b30113de0f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a90f10037c5230d4281abb93c9179e4.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786999ff39b91fac93044fb70679be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b67a008cbc20e42a317acfd632a8052.png)
您最近一年使用:0次
2022-08-22更新
|
552次组卷
|
2卷引用:贵州省遵义市新高考协作体2023届高三上学期入学质量监测数学(理)试题
名校
解题方法
9 . 已知函数
,
R.
(1)若
存在单调递增区间,求
的取值范围;
(2)若
,
为
的两个不同极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42a51bfb55f49d21a8986a4f59695e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb71310ec267ea2c2fc0ccaeb2343d0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](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/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0e7bdd0b28e60c395695dcecd1a61.png)
您最近一年使用:0次
2021-08-04更新
|
981次组卷
|
6卷引用:贵州省遵义航天高级中学2021-2022学年高二下学期第一次月考数学(理)试题
贵州省遵义航天高级中学2021-2022学年高二下学期第一次月考数学(理)试题福建省南平市2020-2021学年高二下学期期末数学试题安徽省合肥市第一中学2021-2022学年高三上学期段一测试文科数学试题云南衡水实验中学2022届高三上学期期中考试数学(文)试题(已下线)第5章《导数及其应用》 培优测试卷(三)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)模块三 大招7 不等式证明——主元法
名校
解题方法
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0851cb3ee044b66e0635528c0f91a524.png)
(1)若
为定义域内的单调递增函数,求
的取值范围;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0851cb3ee044b66e0635528c0f91a524.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f5f7a36e251bbc424ccc127ebb2881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ff8719f0965d2523a6c581e6570502.png)
您最近一年使用:0次
2021-05-10更新
|
510次组卷
|
3卷引用:贵州省遵义市第一中学2022届高三上学期第一次月考数学(理)试题