名校
解题方法
1 . 设函数
,其中
和
是实数,曲线
恒与
轴相切于坐标原点.
(1)求常数
的值;
(2)当
时,关于
的不等式
恒成立,求实数
的取值范围;
(3)求证:对于任意的正整数
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d898c0ea26601b90dccfb8c11ae4712.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:对于任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed08261f7e9b82eb1906cca1abff1a6.png)
![](https://img.xkw.com/dksih/QBM/2017/8/15/1752670428037120/1753289400385536/STEM/36cda1a30cef44fd841f3865b20ba631.png?resizew=3)
您最近一年使用:0次
2 . 已知函数
,其中
.
(1)若
,求证:当
时,
成立;
(2)若
,判断函数
的零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73943a7566c5fdd60e7122c3cdbd869d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0372e386405ede82b72a0f268b741c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4220892627ceb9562b815430a2f8b99a.png)
您最近一年使用:0次
2017-07-12更新
|
278次组卷
|
2卷引用:福建省泉州市泉港区一中2016-2017学年高二下学期期末考试数学(理)试题
3 . 已知函数
为
的导函数.
(Ⅰ)令
求
的单调区间;
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7694913d438b5075bea3515738ac32de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅰ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8211749eaa81821bd9738d067f441b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b727fae2e8d5648700d3b39dfc7860f.png)
您最近一年使用:0次
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebdb25f3eebf5e0314999c8aa7ed43d1.png)
,
在
和
处取得极值,且
,曲线
在
处的切线与直线
垂直.
(1)求
的解析式;
(2)证明关于
的方程
至多只有两个实数根(其中
是
的导函数,
是自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebdb25f3eebf5e0314999c8aa7ed43d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbf3854307b2b6ab937a3e3e40e05a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971905ea129aec0ca7c325f60260c7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd86badb20015aa65328fda1e43a117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a241d6ef06bc899a9dbb28b62c0aec5c.png)
![](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/512f4c29ff276b7f35052ad4cc255ab5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9857fdafea0bb1b836c9bcf1d735d71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
您最近一年使用:0次
2017-05-16更新
|
945次组卷
|
2卷引用:福建省三明市2017届普通高中高三毕业班5月质量检查数学(文)试题
名校
5 . 已知函数
在
处的切线方程为
.
(1)求
的单调区间与最小值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2dcaf9ab62fb0251f0f6e5e7d87d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c887da0c850acf41ab249cc262ae39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306b6e79f39d396ad32493c62224d8b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5667c0ed1db3b4c34c8978d7b2d362.png)
您最近一年使用:0次
2017-05-09更新
|
1905次组卷
|
5卷引用:福建省泉州市2017届高三高考考前适应性模拟(一)数学(理)试题
名校
6 . 已知函数
,其中
为自然对数的底数.
(1)函数
的图象能否与
轴相切?若能与
轴相切,求实数
的值;否则,请说明理由;
(2)若函数
在
上单调递增,求实数
能取到的最大整数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8b007d1a1a9c15ae78ae329f113c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c3a071e25281dee9a0ef0b75dd550c2.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc3658b6ac8f93da2da065c0a11abfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-04-29更新
|
207次组卷
|
2卷引用:福建省莆田第六中学2017届高三下学期第二次模拟数学(理)试题
名校
7 . 已知函数f(x)=(ax-1)ex,(a∈R).
(Ⅰ)讨论f(x)的单调性;
(Ⅱ)当m>n>0时,证明:men+n<nem+m.
(Ⅰ)讨论f(x)的单调性;
(Ⅱ)当m>n>0时,证明:men+n<nem+m.
您最近一年使用:0次
2017-04-11更新
|
1045次组卷
|
8卷引用:2017届福建省高三4月单科质量检测数学文试卷
2017届福建省高三4月单科质量检测数学文试卷河北省定州中学2017届高三下学期第二次月考(4月)数学试题湖南省岳阳市一中2018届高三上学期第一次月考数学(文)试题陕西省吴起高级中学2018届高三上学期期中考试数学(文)试题陕西省宝鸡中学2019届高三年级第二次模拟数学(文科)试题【市级联考】陕西省宝鸡市2019届高三高考模拟检测(二)数学(文科)试题安徽省阜阳市太和中学2021届高三下学期高考押题文科数学试题(已下线)专题3-6 导数压轴大题归类(1)-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
解题方法
8 . 已知
,
内切
于点
是两圆公切线
上异于
的一点,直线
切
于点
,
切
于点
,且
均不与
重合,直线
相交于点
.
(1)求
的轨迹
的方程;
(2)若直线
与
轴不垂直,它与
的另一个交点为
,
是点
关于
轴的对称点,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc9c6367bc4ea5531d8897866650654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e69fd92eceb49fed10c4b50723d13d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ba050bb69ab55bdcb96f935f5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff571c72c041d8668b4d2754679f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e69fd92eceb49fed10c4b50723d13d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f97913e1af1e6c793f7edfe6b2114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ba050bb69ab55bdcb96f935f5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca00309261a540934d9b3ed9ba05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6eca278d6d9bbe688b1d8fd37f67e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2cda9e5690d90d24c318895db59a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59565e25fe3159700364a73fa6a71512.png)
您最近一年使用:0次
9 . 函数
.
(1)讨论
的单调性;
(2)当
在
上单调递增时,证明:对任意
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f6aef47d0b3722fa9783ab0cc643e.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab89b4cbee1764467262836d6d4d91c2.png)
您最近一年使用:0次
10 . 已知函数
.
(1)若直线
与曲线
恒相切于同一定点,求
的方程;
(2)当
时,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2c51369c404a1e3485002ef9d26021.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da74ec6ccbe7f2948b624d2bf83e3711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-03-13更新
|
844次组卷
|
2卷引用:2017届福建省泉州市高三3月质量检测数学理试卷