名校
解题方法
1 . 已知函数
.
(1)若
单调递增,求
的值;
(2)设
是方程
的两个实数根,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309c63092890ba2dc161bd00908cce75.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed928f3b9509ffb779bf077fbba9d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次
2023-11-27更新
|
394次组卷
|
3卷引用:湖南省长沙市宁乡市第一高级中学2021届高三下学期第一次模拟考试数学试卷
名校
2 . 已知
,
.
(1)若
在其定义域上为减函数,求
的取值范围;
(2)若函数
在
上有且只有1个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755971d4df19ecddedbbdb7c2ea61e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d217c7b12e12e5fb67472452518859ec.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67426f1543d483813f979a5fb14e8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bb82965d5b3c7426b5fc82f5edeb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-08-09更新
|
362次组卷
|
3卷引用:陕西省西安市周至县2020-2021学年高三一模理科数学试题
名校
解题方法
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d370904f335ee2471c7635b1da771796.png)
(1)若
,求函数
的极值;
(2)若
在
内为单调递增函数,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d370904f335ee2471c7635b1da771796.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](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/ed6d804ef44bfc64f824b0ccef71765e.png)
您最近一年使用:0次
2023-05-29更新
|
713次组卷
|
2卷引用:陕西省咸阳市兴平市南郊高级中学2021-2022学年高三上学期二模文科数学试题
名校
4 . 已知函数
.
(1)讨论函数
的单调性;
(2)若对任意
,
都有
成立,其中
且
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068132ef9604287c220c731012efec01.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d7c85749a181ee97a54bde7dfb1537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f0ba205794d6fbb4a6b4d4ad6a499c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d1821d2bc56bf8ac6789fcfffef9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
.
(1)若
在
上单调递增,求
的取值范围;
(2)若
在
上存在极值点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28cb07d617bf1ea6b5b4c979022c57ef.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69889916683f17377ca68f04a4c2e61.png)
您最近一年使用:0次
2022-01-07更新
|
565次组卷
|
2卷引用:四川省凉山州2021-2022学年高三上学期第一次诊断性检测数学(理)试题
2021·全国·模拟预测
解题方法
6 . 已知函数
(
).
(1)若
在
上是增函数,求
的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c93039df7a8e3ef5a591a8b282f49d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23015ce5a0e51592eaa9f1eae8547eaf.png)
您最近一年使用:0次
2021-12-03更新
|
755次组卷
|
5卷引用:2022年全国著名重点中学领航高考冲刺试卷(九)
2021·全国·模拟预测
名校
解题方法
7 . 已知函数
,
.
(1)设
,若函数
是定义域上的减函数,求
的取值范围;
(2)已知函数
的图象上任意两点
,
,
,设直线
的斜率为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed9ee8ded235550ac39ed5ae767b8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31017c483ddabb71ea26b7bf64d58c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e0cf9f0a021abfa0c5602b97a1e1f2.png)
您最近一年使用:0次
名校
8 . 已知函数
.
(1)当
时,求函数
的图象在
处的切线方程.
(2)若函数
在定义域上为单调递增函数.
①求整数
的最大值;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5807f807737f3a31a849f0ccc60f33.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dfb495fb337b2c28b84e2a6c9385d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①求整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773d5a5be51017b4b06f4a4d572dd6aa.png)
您最近一年使用:0次
2021-10-08更新
|
1722次组卷
|
3卷引用:2021年全国高考冲刺压轴卷(四)理科数学试题
解题方法
9 . 已知函数
(
).
(Ⅰ)若函数
在
上单调递增,求实数
的取值范围;
(Ⅱ)若函数
有两个不同的极值点
,
,且
,判断
是否有最小值,若有求出最小值;若没有说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f78e6ee8bc80d5112b1d414aff629f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(Ⅰ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅱ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c58e47b409b049b5729efed3226c9c.png)
您最近一年使用:0次
解题方法
10 . 已知函数
,其中
,
.
(1)若
,证明:
;
(2)若
单调递增,求a的取值范围;
(3)当
且
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb072ab1245ee62cdb2283ac9536b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27794407a3d82a6746f7e0871051f486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2c56ae91b6b5471006f9814972931b.png)
您最近一年使用:0次