名校
1 . 已知函数
.
(1)若
在区间
内存在极值点
,求实数
的取值范围;
(2)在(1)的条件下,求证:
在区间
内存在唯一的零点
,并比较
与
的大小,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d7695f4363f9e3d5f8e63813e01a73.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8f96ee3ef89abc201ddd6447cf0b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)在(1)的条件下,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267572d2dff2dc38cf9251b7f33a3e61.png)
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2023-05-20更新
|
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2卷引用:江西省重点中学协作体2023届高三第二次联考数学(理)试题
名校
解题方法
2 . 已知函数
.
(1)证明:函数
在
上有且只有一个零点;
(2)当
时,求函数
的最小值;
(3)设
,若对任意的
恒成立,且不等式两端等号均能取到,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0efc5fda061b4ed54baebd31ae741d.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d795e3d9afa935e2741c75526a8c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adae3f8382c7456d50855aaf9a12b37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
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2023-05-06更新
|
2107次组卷
|
6卷引用:江西省南昌市新建区第二中学2024届高三上学期8月开学学业水平检测数学试题
江西省南昌市新建区第二中学2024届高三上学期8月开学学业水平检测数学试题浙江省温州市2023届高三下学期5月第三次适应性考试(三模)数学试题广东省深圳外国语学校2022-2023学年高二下学期期末数学试题(已下线)专题05 导数大题上海外国语大学附属浦东外国语学校2024届高三下学期3月月考数学试题(已下线)高二数学下学期期末押题试卷02(测试范围:新高考全部内容)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
3 . 已知函数
.
(1)讨论函数
在
上的零点个数;
(2)当
且
时,记
,探究
与1的大小关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81eeb610596766eb3d36bf33f603953.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499a8449e8bb253065463c23f3ff5860.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff537b9287dffb28e89bfc2bf5ed723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2a14d9c7f3d948525c2660db272223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.png)
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2023-05-02更新
|
709次组卷
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6卷引用:江西省智慧上进联盟2022-2023学年高二下学期期中调测试数学试题
4 . 已知函数
.
(1)讨论
的极值;
(2)若
有两个零点
,求实数
的取值范围,并求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89a7d7ac06e03fc2714de0557bf80e2.png)
(1)讨论
![](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/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6752d13f5a4a5023e8e38c58860b06.png)
您最近一年使用:0次
5 . 已知函数
,其中
,
(1)若
,
(i)当
时,求
的单调区间;
(ii)曲线
与直线
有且仅有两个交点,求
的取值范围.
(2)证明:当
时,存在直线
,使直线
是曲线
的切线,也是曲线
的切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3373d211a4a1bf81e1ebfb146fcddf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3a42b6fd4fff031515c4845db4a947.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(ii)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932e474e861cbef4611e8bdebf2814f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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2023-04-26更新
|
997次组卷
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2卷引用:江西省万安中学2024届高三上学期开学考试数学试题
6 . 已知函数
.
(1)若
成立,求实数
的取值范围;
(2)证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1effc3ed209606a8533c83815da681d7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2113985dff34cfe734d4827f84ad833f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2967ed649696f1a427809b4dddba34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e0bba9da466d81395d05bc47d95a9a.png)
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2023·江西吉安·一模
7 . 已知函数
,
的导函数为
.记函数
在区间
内的零点为
,
.
(1)求函数
的单调区间;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc67014a5504d171ad11414457c177ea.png)
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a332a404d9097ff95e0e5c59e0812cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3703423fab8a609508d2ca856625fbb.png)
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8 . 已知函数
.
(1)当
时,求曲线
在点
处的切线与两条坐标轴围成的三角形的面积;
(2)若函数
有三个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef64b75b408b846d80ef26f17b7dec4d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3c5ed65fc64235532313e51cf8311b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-04-07更新
|
822次组卷
|
4卷引用:江西省龙南中学2022-2023学年高二下学期期中数学试题
江西省龙南中学2022-2023学年高二下学期期中数学试题湘豫名校联考2023届高三4月二模理科数学试题河南省周口市2023届高三下学期4月模拟理科数学试题(已下线)模块八 专题11 以函数与导数为背景的压轴解答题
9 . 已知函数
,
.
(1)若直线
与曲线
相切,求a的值;
(2)用
表示m,n中的最小值,讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8cf86a61f27e83a25073cbe1c06527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4006cb607c3244dc446595067696510.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0898d7174604fa223558cb25b4c78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f230ef8f16dbda82952f9012c82295e5.png)
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2023-03-26更新
|
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6卷引用:江西省九江市2023届高三高考二模数学(理)试题
江西省九江市2023届高三高考二模数学(理)试题江西省上饶市六校2022-2023学年高二下学期5月联考数学试题(已下线)专题07 导数(已下线)专题04函数与导数(解答题)(已下线)重难点突破09 函数零点问题的综合应用(八大题型)(已下线)【一题多变】取大取小 分类讨论
10 . 已知函数
,
.
(1)当
时,证明:
;
(2)当
时,判断
零点的个数并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea04b72efca9861a248432a23bb965c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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