1 . 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
|
612次组卷
|
4卷引用:广东省东莞市2022-2023学年高二下学期期末数学试题
2 . 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)
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名校
3 . 已知函数
,
在
处取极大值,在
处取极小值.
(1)若
,求函数
的单调区间;
(2)在方程
的解中,较大的一个记为
,在方程
的解中,较小的一个记为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fdf56a87c52a195df737c1fdc71035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)在方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ffaf77e38607c44aa74739c79537fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994a70ca0d114c96d56006df0ba14c1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e076c1927e1f4b1a585a5ea588a4f487.png)
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解题方法
4 . 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)
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5 . 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
6 . 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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7 . 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
|
299次组卷
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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
8 . 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
9 . 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)
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2023-03-26更新
|
1598次组卷
|
5卷引用: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
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07 导数(已下线)专题06 函数与导数(已下线)专题19 押全国卷(理科)第21题 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
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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