名校
解题方法
1 . 设函数
.
(1)若
,求证
有极值,求方程
的解;
(2)设
的极值点为
,若对任意正整数
都有
,其中
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85aa2e4d5f2fe4f49d72e2302a1585d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
(2)设
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed085cc685f0bf1b3df2ed16e04ccea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b00438433719b82971f9fe309e04b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
2 . 给出定义:设
是函数
的导函数,
是函数
的导函数,若方程
有实数解
,则称(
)为函数
的“拐点”.经研究发现所有的三次函数.
都有“拐点”,且该“拐点”也是函数
的图像的对称中心,已知函数
(1)求出
的对称中心;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c553558c1640e17b0c67395627d488c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f087ded8039eedaa8aa724b81ec393e9.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88afe5c5be8dc12217ccbef588cc61c.png)
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3 . 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)
您最近一年使用:0次
解题方法
4 . 已知函数
.
(1)若
,求方程
的解;
(2)若
有两个零点且有两个极值点,记两个极值点为
,求
的取值范围并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6fcc141688e104bfeba4b866d7873e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9694eaaa274ed8e3774a100aff5f101.png)
您最近一年使用:0次
2023-03-26更新
|
1597次组卷
|
5卷引用:专题07 导数
(已下线)专题07 导数(已下线)专题19 押全国卷(理科)第21题 导数浙江省温州市普通高中2023届高三下学期3月第二次适应性考试数学试题(已下线)专题06 函数与导数福建省三明市优质高中校2022-2023学年高二下学期期中联考数学试题
名校
5 . 已知函数
在
处取得极值7.
(1)求
的值;
(2)求函数的单调性及极值;
(3)若关于
的方程
在
上恰有2个不同的实数解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d5a008df42ec0fc435932b2efc9fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)求函数的单调性及极值;
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2cf7f3f8b79fdad44ee007a2404217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
6 . 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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7 . 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)
您最近一年使用:0次
解题方法
8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f8cd466fc33dc01e224f8d9cc097b0.png)
(1)当
时,求满足不等式组
的
的取值范围;
(2)当
时,不等式
恒成立.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f8cd466fc33dc01e224f8d9cc097b0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef932877eef10ef2974ce9e29ea47f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737c165baced95d7095d9f918a9cc110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8238f660e6b686ed05405f1ccdf6a0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
9 . 函数
.
(1)若
有三个解,求
的取值范围;
(2)若
,且
,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471b38a51827c82982db783278806192.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12ae52a789c95f75d6519a48472db4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0344c84e1050f3cd0856a94450c82652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928dc7dde8b5c99389ae90fcbfa78506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fea6db9a25e472b621eb94281e40d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)当
时,求函数
的极值;
(2)若关于x的方程
在
无实数解,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3021befc8618d74375b2eadba940f07c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb95fe8ab68d221c70acdee5451cc73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
您最近一年使用:0次
2022-09-14更新
|
994次组卷
|
9卷引用:江西省上饶市第一中学2022届高三5月模拟考试数学(文)试题
江西省上饶市第一中学2022届高三5月模拟考试数学(文)试题(已下线)第12节 导数的综合应用(已下线)专题10导数与函数的极值、最值-2022年新高三数学暑假自学课精讲精练(已下线)4.3 利用导数求极值最值(精练)-【一隅三反】2023年高考数学一轮复习(提升版)(新高考地区专用)(已下线)第15讲:第三章 一元函数的导数及其应用(测)(基础卷)-2023年高考数学一轮复习讲练测(新教材新高考)天津市南开中学2023届高三上学期统练2数学试题四川省仁寿县文宫中学2022-2023学年高三9月月考数学(文)试题宁夏银川一中2023届高三上学期第二次月考数学(文)试题黑龙江哈尔滨工业大学附属中学校 2021-2022学年高二下学期期末理科数学试题