1 . 已知函数
.
(1)讨论函数
的单调性;
(2)求函数
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0580ca9d38479a5783f5657ab4c01a1.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc7149558748931adb07aad426b060d.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f178aafef1a74d224f7e90f8ceeed914.png)
您最近一年使用:0次
2023·全国·模拟预测
2 . 一类项目若投资1元,投资成功的概率为
.如果投资成功,会获得
元的回报
;如果投资失败,则会亏掉1元本金.为了规避风险,分多次投资该类项目,设每次投资金额为剩余本金的
,1956年约翰·拉里·凯利计算得出,多次投资的平均回报率函数为
,并提出了凯利公式.
(1)证明:当
时,使得平均回报率
最高的投资比例
满足凯利公式
;
(2)若
,
,求函数
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893e658908683584084ea8cd2b1abb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e4dfb68af91a58e45ca8596abc3d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821289d70c0fb192f97cd7e0c4030d3b.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882d11ef98daf356e7ce70c24d4b9cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25770560bdfb28b2b79f2900084057e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee70e500750f7aeef9a15557433ad3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
您最近一年使用:0次
2024-01-17更新
|
842次组卷
|
5卷引用:安徽省六安市金寨第一中学2024届高三上学期期末适应性考试数学试题(二)
名校
解题方法
3 . 设函数
,
,
.
(1)求函数
在
上的单调区间;
(2)若
,
,使
成立,求实数a的取值范围;
(3)求证:函数
在
上有且只有一个零点
,并求
(
表示不超过x的最大整数,如
,
).
参考数据:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89231f0078f75ad0193f9aec97b9286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3e40a1b375c50331403283bfd7139b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0167434c2c1a16e59e89d436ac0a1278.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fc78bba43797d2f81cb912f2d05c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac0afd127806b03435a649606544fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe53bb5e833f83c2d8290d195fabf02b.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5e51f08fcfaa95b58f3a14c8250a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41667e2986ec718cabeeb1088794ed67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04309e875209bde5b87438535ea3b1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977353e0326dc27334a2940f1149e973.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e143d31a5ae4d2fb8cba2466bae1fe54.png)
您最近一年使用:0次
2024-01-06更新
|
659次组卷
|
6卷引用:安徽省合肥市合肥一中肥东分校2023-2024学年高一上学期期末数学试题
名校
4 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313a8876020169bd7f1bda1148b31ab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130fa1ad810b53f0ee1d7cfe00706381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-05-05更新
|
572次组卷
|
3卷引用:安徽省太和中学2022-2023学年高二下学期选修模块检测数学试题
5 . 已知函数
.
(1)求
的导函数
的单调区间;
(2)若方程
(
)有三个实数根
,且
,求实数 a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e857fc101bb0fbb456f1efb6748032.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdcb20fdc8bab941d857045172f20a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f20fd3e0a644e65ca4c817bcf02fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae937a39534e192c13d1791430e75ea.png)
您最近一年使用:0次
2023-01-14更新
|
485次组卷
|
2卷引用:安徽省阜阳市临泉第一中学2022-2023学年高三上学期1月期末理科数学试题
6 . 已知函数
.
(1)若
在
上是增函数,求实数
的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8163ef24d8945d690949e4a0a85077f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f25bcb0e6fb29e378fd3de0cd26056.png)
您最近一年使用:0次
2022-09-01更新
|
544次组卷
|
3卷引用:安徽省卓越县中联盟2022-2023学年高三上学期开学考试数学试题
名校
解题方法
7 . 若点
在函数
的图象上,且满足
,则称
是
的
点.函数
的所有
点构成的集合称为
的
集.
(1)判断
是否是函数
的
点,并说明理由;
(2)若函数
的
集为
,求
的最大值;
(3)若定义域为
的连续函数
的
集
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ef0287740211d65da72c0e494e630c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4966e5af166b69a0a38a98abf555b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c111ae39998037ad9c2eef5a892b3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b820f749904501fafc23018b528ed82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)若定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/262ea17a76ec2b15e9f5c96e42ca4b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d27fb6dea56ea845f338fce3d432af9.png)
您最近一年使用:0次
2022-07-07更新
|
1987次组卷
|
8卷引用:安徽省安徽师范大学附属中学2022-2023学年高一下学期3月月考数学试题
安徽省安徽师范大学附属中学2022-2023学年高一下学期3月月考数学试题北京市海淀区2021-2022学年高一下学期期末练习数学试题上海市复旦大学附属中学2023届高三上学期9月月考数学试题河南省周口市淮阳区淮阳中学2022-2023学年高一上学期期末数学试题(已下线)第5章 三角函数(基础、典型、易错、压轴)分类专项训练(2)广西桂林市第十八中学2023-2024学年高一下学期4月月考数学试题(A卷)北京市第十四中学2023-2024学年高一下学期期中检测数学试卷(已下线)上海市高一下学期期末真题必刷04-期末考点大串讲(沪教版2020必修二)
名校
8 . 已知实数
,设函数
,
是函数
的导函数.
(1)证明:
存在唯一零点;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4e254f5e683d3b4bf99b03c5c160c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3704125881727a906c7db5ae11b2b01.png)
您最近一年使用:0次
2022-03-11更新
|
370次组卷
|
2卷引用:安徽省淮南第二中学2021-2022学年高二下学期博雅杯素养挑战赛数学试题
名校
9 . 已知函数
.
(1)若
,求证:
恒成立;
(2)当
时,求
零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c07d25c35ce88f83962403fd7dc797.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d212226826bb1d283046f73311a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)求函数
的极值点;
(2)若函数
的图象与
的图象有3个不同的交点,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7baac46881798c16564d0e59e94afbe.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3c04cfed27843087dd57d1a3ffb384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次