解题方法
1 . 已知函数
.
(1)求函数
的单调区间和极值;
(2)若方程
的两个解为
、
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ed99a74e126a05cb520f19c094020.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff9681471371af6e3d0934caee1004.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/546a1ee9369c1c238e3e9ff1bb4a236e.png)
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2 . 已知函数
.
(1)求函数
在
处的切线方程;
(2)若
是
的极值点,且方程
有3个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66aa600e8ebc54042affceac4efeaeb7.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31bc0c34811edba74dae3fcaed8f577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-07-08更新
|
609次组卷
|
3卷引用:广东省东莞市2022-2023学年高二下学期期末数学试题
3 . 已知
,
(1)当
时,求函数
在点
处的切线方程;
(2)当
时,求函数
的单调区间;
(3)当
时,方程
在区间
内有唯一实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed99d4c101cf81761402a2e34b3fca5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45771f0bf8148df998a7d4c47aae6092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9a3b952c78347f2dff530df17a175a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf613d5ed2a4b75ee70638f28fd9f44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)讨论函数
的单调性;
(2)若关于x的方程
有两个实数解,求a的最大整数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59f33469e58031e1aa348877d028937.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
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2023-02-16更新
|
1579次组卷
|
9卷引用:安徽省合肥市2023届高三下学期第一次教学质量检测数学试题
安徽省合肥市2023届高三下学期第一次教学质量检测数学试题(已下线)模块十三 函数与导数-2(已下线)专题05导数及其应用(解答题)江西省丰城中学2022-2023学年高三下学期3月月考文科数学试题(已下线)专题21利用导数研究函数零点(已下线)专题16 押全国卷(文科)第20题 导数(已下线)第5章 导数及其应用(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020选择性必修第二册)河南省鹤壁市高中2022-2023学年高二下学期第五次段考数学试题(已下线)第五章 导数及其应用 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)
5 . 已知函数
,
.
(1)
,
,求
的最小值;
(2)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4ee544faff9e49a41d9b69827501b.png)
①证明:
;
②若方程
有两个不同的实数解
,
证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d23c80f11dcb3f7537c88cbd76a1267.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f042768ad824aad2aed73a44193856c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4ee544faff9e49a41d9b69827501b.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3799b7e05fda170b8f661643a1685bbc.png)
②若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32051bf94998f88eecff75846cc750b0.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/901a1ca166c6ddf5ae7a7cb7d66431b0.png)
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6 . 已知函数
.
(1)若
时,函数
有2个极值点,求
的取值范围;
(2)若
,
,方程
有几个解?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd5d894cf062351f780fbe4369cea7a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ff4b5cce546fb285ab03ced957ce41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515f88ff8fa1cad560307bd2b2e13fcb.png)
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7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f70ec2e471997fb193188d306cffe.png)
(1)求
在
处的切线方程;
(2)若
在定义域上有两解
,求证:
①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f70ec2e471997fb193188d306cffe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cfada8fd642ddf968bfd4228d48ec3.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed7932a5ee7f639c53e6eb0a007eb91.png)
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2023-01-09更新
|
743次组卷
|
2卷引用:河北省衡水市第二中学2023届高三上学期一模数学试题
名校
解题方法
8 . 设函数
,曲线
在原点处的切线为x轴,
(1)求a的值;
(2)求方程
的解;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdb851dc97c4ad46840967fb55d737f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)求a的值;
(2)求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0884469ef5f3e6ad7acaae339ab0d69.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e083f90a56a3c783b7c12ba77aae0ade.png)
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9 . 已知曲线
在点
处的切线方程为
.
(1)求a,c的值;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7823aa2ac66c00ce0f260f3147eb6a.png)
(3)若关于x的方程
有两个实数解
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e34dc94a3d9dc4677f75e0aac8e98da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96f623802cd414e590247155ad0d62b.png)
(1)求a,c的值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7823aa2ac66c00ce0f260f3147eb6a.png)
(3)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c9639ad329a88d242c2d6f37d7c456.png)
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2023-04-03更新
|
298次组卷
|
2卷引用:湖北省咸宁市鄂南高级中学2022-2023学年高二下学期阶段性检测(9)数学试题
解题方法
10 . 已知函数
与函数
有相同的极值点与极值.
(1)求a,b;
(2)若方程
与
分别有两个解p,q(
)和r,s(
).
①分别用p,q表示出r,s;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7275d5d8dc96e8f717905b3b829917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477bdd62660801ac1dfa2d60ba333cd6.png)
(1)求a,b;
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2818807dce7e9ec5514de572c3cc644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4610754dff007c541aa4887d8705329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25109e1cbcdb7f8cedd0422525a1cdb.png)
①分别用p,q表示出r,s;
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2c12355c99c2e113b23e748b768eaf.png)
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