名校
1 . 已知函数
,
.
(1)求
的单调区间;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc1e1eda1e062dc9c898622072f0495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1610bcd07b02c4ed7184ad586b88f373.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375d897a1f137d6c6704d24f9b4b0948.png)
您最近一年使用:0次
2023-11-15更新
|
385次组卷
|
5卷引用:辽宁省铁岭市一般高中协作校2023-2024学年高三上学期期中考试数学试题
名校
解题方法
2 . 已知函数
.
(1)当
时,
恒成立,求实数
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec74022c3d20a1e7017e84920f30cfd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8291ca77106b0bcd3de09a4b9e63504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1dd548055a06de23bf929f6eb1896d1.png)
您最近一年使用:0次
名校
3 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455737c14aa0d487847d78c785c17a46.png)
(1)若
有两个零点,求
的取值范围;
(2)若方程
有两个实根
、
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455737c14aa0d487847d78c785c17a46.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed15647423ebaba1f4d9373b46172e12.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/684bcf84f0a266515bfafde0da903050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab79778de8353f2b37f13b8e8af1f10.png)
您最近一年使用:0次
2023-11-11更新
|
627次组卷
|
4卷引用:辽宁省北镇市第二高级中学、第三高级中学2024届高三上学期第四次月考数学试题
4 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf255b913e8b08681dda42380e03115.png)
(1)
,
,求实数
,
的值;
(2)利用
,证明:当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a70580f34db8f1b309287195c5ac7e7.png)
(3)证明:若
,其中
,
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8509c6684cb06366f3a1b9e391a3d7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf255b913e8b08681dda42380e03115.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860c8bee8ca79c135861311fa4fddb0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b7c973fd05c6dbfef9adf37040c53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)利用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9098338d53471dd9041390613b25171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a70580f34db8f1b309287195c5ac7e7.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1020297598b474821bdbb8a33de986e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc69868d5be72f71f9aa2099c84e1e61.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
(
为自然对数的底数).
(1)若
,求实数
的值;
(2)证明:
;
(3)对
恒成立,求
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da80426b4a667a7e2d5073408da1dbaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dce060801a5814dd2c812c578581e88.png)
(3)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a08c1678252718ea5cc727d476920fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-01-16更新
|
920次组卷
|
3卷引用:辽宁省大连市2024届高三上学期双基测试数学试题
名校
6 . 已知函数
.
(1)若
,当
时,证明:
.
(2)若
,证明:
恰有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454a1d6d83fa3bd5e63eccd676fbfc84.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.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/d7cfada8fd642ddf968bfd4228d48ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2024-02-29更新
|
2749次组卷
|
6卷引用:辽宁省沈阳市辽宁实验中学2024届高三下学期高考适应性测试(二)数学试题
7 . 已知函数
,曲线
在点
处的切线方程为
.
(1)求
的值并讨论
的单调性;
(2)设
为两个不相等的正数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99bede9abb43cf6dabb90a0cc80c4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000eef050602fcd0f24777edaeab3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4844d12d7b0a4c6bcdc3e3ab5709fe.png)
您最近一年使用:0次
2023-08-23更新
|
234次组卷
|
2卷引用:辽宁省大连市大连开发区十中2024届高三上学期期中数学试题
名校
8 . 已知函数
.
(1)当
时,求
的单调区间;
(2)当
时,若不等式
恒成立,求
的取值范围;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae19d7b49be015e2ef80f1ddc78378a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc895959e9bc92294dc9dd2263dbf0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8d5e61351e8a57f702e9ae66d146d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68207a3154bd827a6647075efda61f70.png)
您最近一年使用:0次
2023-10-07更新
|
736次组卷
|
4卷引用:辽宁省六校协作体2024届高三上学期期中联考数学试题
名校
解题方法
9 . (1)已知函数
及其导函数
的定义域均为
,设
是曲线
在点
处的切线的方程. 证明:当
是增函数时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)已知
,设
的最大值为
,证明:
.
(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4f6388b5809b156ce9289dc5846920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38da3eb873f57196dc4fda166a1db16e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5b440818076e1e7fa8800fa848ae06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08320e6e96f872f1fcf6ad8096ebaa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01a1e17f4bd23682465df5b42309725.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06341cc14870ff71931aae0d3d78abfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ebbae545ae1e8e4b06bf861fa53e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a2f2d080ac398bea650aecd40ca8ab.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06678b48ba1d12f0748bbed1a9d27478.png)
(1)若
,证明:
;
(2)设
,若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06678b48ba1d12f0748bbed1a9d27478.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62b74522d84abe0dc4d5983694ea748.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1411c719bc69f11b60e566baa09f383c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4fe5e35859136dafc3373c01009f24.png)
您最近一年使用:0次
2023-09-29更新
|
2062次组卷
|
4卷引用:辽宁省沈阳市东北育才学校2024届高三第三次模拟考试数学试题
辽宁省沈阳市东北育才学校2024届高三第三次模拟考试数学试题湖北省武汉市华中师范大学第一附属中学2023届高三5月适应性考试数学试题(已下线)第六章 导数与不等式恒成立问题 专题六 单变量恒成立之参变分离法 微点4 单变量恒成立之同构或放缩后参变分离综合训练吉林省松原市前郭尔罗斯蒙古族自治县第五高级中学2023-2024学年高三上学期10月月考数学试题