名校
解题方法
1 . “拐点”又称“反曲点”,是曲线上弯曲方向发生改变的点.设
为函数
的导数,若
为
的极值点,则
为曲线
的拐点.
已知曲线C:
.
(1)求C的拐点坐标;
(2)证明:C关于其拐点对称;
(3)设
为C在其拐点处的切线,证明:所有平行于
的直线都与C有且仅有一个公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7013f94a41df38d395aaa830559ae31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2848ae11c9a59b86a60f206f69efcb19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7013f94a41df38d395aaa830559ae31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688fe159aac6cd2422b0f834e2b2338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c087cba6516cfb66c9d346df7e8a24b.png)
已知曲线C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497260109e600d68e2a84b20d791de06.png)
(1)求C的拐点坐标;
(2)证明:C关于其拐点对称;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
为定义在
上的奇函数.
(1)求实数
的值;
(2)(i)证明:
为单调递增函数;
(ii)
,若不等式
恒成立,求非零实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd492d001a460384ca5c5ad7211561f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d75ab6ff78fda13e8f5d11d7a3d8bd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-02-04更新
|
546次组卷
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3卷引用:陕西省西安铁一中学2023-2024学年高一上学期期末考试数学试卷
名校
3 . 已知函数
与
具有如下性质:
①
为奇函数,
为偶函数;
②
(常数
是自然对数的底数,
).
利用上述性质,解决以下问题:
(1)求函数
与
的解析式;
(2)证明:对任意实数
,
为定值;
(3)已知
,记函数
的最小值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df412ae6aa217d7eaa8dd3b88faa9b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
利用上述性质,解决以下问题:
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c55cc1394290408de681b3e23865ca.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647f47ff99c3aadb742b07fc39c7ad7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
且
.
(1)判断
的奇偶性并给出证明;
(2)若对于任意的
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a03272cb8d8fb37896c6fda5f7d8f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1261e861efb873b6ad37010bb8aec33d.png)
您最近一年使用:0次
5 . 已知函数
,
.
(1)判断函数
的奇偶性,并说明理由;
(2)当
时,证明:函数
在
上单调递减;
(3)若对任意的
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0cb86fc09ac3f21b960718acf51c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cfada8fd642ddf968bfd4228d48ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40beaf3b21a8d7d06b46d473e99d1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c91f17f6001a1341711dc4d0473035c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
6 . 定义在
上的函数
,对任意的,都有
成立,且当
时,
.
(1)求
的值;
(2)证明:
在
上为增函数;
(3)当
时,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f68c6ed09e483db6edf0b4caf5e252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9892a2fe8112fc636104312092cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f68c6ed09e483db6edf0b4caf5e252.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57457379efecec3a8f98377bc5c65d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724b3a8e2ec7e73c9181e23bda9ac881.png)
您最近一年使用:0次
2023-11-10更新
|
664次组卷
|
5卷引用:陕西省安康市名校2023-2024学年高一上学期期中联考数学试题
陕西省安康市名校2023-2024学年高一上学期期中联考数学试题江苏省南通市启东市东南中学2023-2024学年高一上学期期中数学试题江苏省连云港市灌云县第一中学2023-2024学年高一上学期期中阶段检测数学试题(已下线)专题03 抽象函数单调性的证明及解不等式(期末大题2)-大题秒杀技巧及专项练习(人教A版2019必修第一册)(已下线)专题04 函数的性质与应用2-期末复习重难培优与单元检测(人教A版2019)
名校
7 . 已知函数
,其中
.
(1)若
,求
的值;
(2)判断函数
的零点个数,并说明理由;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8db6cdacc8e4071c6f2780f3da9ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fc5cec42e2884e91c299c480739334.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36825543013336c9df727bc51ff62c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ac925c426d50a3d5901effe66dc470.png)
您最近一年使用:0次
2023-06-22更新
|
256次组卷
|
2卷引用:陕西省西安市铁一中学2022-2023学年高二下学期期末理科数学试题
8 . 已知函数
.
(1)若
,求不等式
的解集;
(2)若
,证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2cb26c8b2ee4296797abb6a70c97fd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](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/28041c5e5949c193468e398cf814cbdf.png)
您最近一年使用:0次
2023-07-11更新
|
338次组卷
|
5卷引用:陕西省汉中市2022-2023学年高二下学期期末理科数学试题
名校
解题方法
9 . 已知函数
(
,且
).
(1)证明:
;
(2)若
,
,
,求a的值;
(3)
,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d76ee3b131ecd6aa1aacf7fb7b3eb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ce07c46c82b60e1a00685283746a9c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb8424a4bccc0f58edb80e83ddb7c96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69467015868cacd78ae8fabec7d58ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f05f93b42ed86815f875aafa958e89.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa139aad70ad1ac124affc3fe5d75c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8b9938de49594044e10b67d662a89d.png)
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2023-07-01更新
|
585次组卷
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3卷引用:陕西师范大学附属中学2022-2023学年高一下学期期末数学试题
陕西师范大学附属中学2022-2023学年高一下学期期末数学试题江苏省南通市海安市2020-2021学年高一上学期学业质量监测数学试题(已下线)第四章 指数函数与对数函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)
解题方法
10 . 已知
是定义在
上的奇函数,其中
、
,且
.
(1)求
、
的值;
(2)判断
在
上的单调性,并用单调性的定义证明;
(3)设
,若对任意的
,总存在
,使得
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06295745406e6bf8f5af9a74fbf2807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726c078ca626f64e0d02c2666d8af105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9da4fdfdddc259dcef9fdd4b826b64.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb8b52b9f71d8cc6e86c7d9a8a47a16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f985718530cae9003dd401c044ef3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a49684ba67f71171321586f1a77ad4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-02-21更新
|
932次组卷
|
8卷引用:陕西省渭南市富平县蓝光中学2023-2024学年高一上学期1月期末检测数学试题
陕西省渭南市富平县蓝光中学2023-2024学年高一上学期1月期末检测数学试题广东省揭阳市惠来县2022-2023学年高一上学期期末数学试题新疆兵团地州学校2022-2023学年高一上学期期末联考数学试题(已下线)3.2.2 函数的奇偶性(精练)-《一隅三反》(已下线)专题3.8 函数的概念与性质全章综合测试卷(提高篇)-举一反三系列(已下线)第三章 函数的概念与性质(压轴题专练)-速记·巧练(人教A版2019必修第一册)(已下线)高一上学期期末数学试卷(提高篇)-举一反三系列(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列