已知函数
.
(1)当
时,求曲线
在点
处的切线与两坐标轴所围成三角形的面积;
(2)若
没有零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12bce0e430e47c12183a3a814d2b8ec.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
2023·内蒙古包头·一模 查看更多[6]
内蒙古包头市2023届高三下学期一模理科数学试题(已下线)内蒙古包头市2023届高三一模理科数学试题(已下线)专题05函数与导数(解答题)(已下线)第四章 导数与函数的零点 专题四 导数中隐零点问题 微点3 导数中隐零点问题(三)福建省厦门市厦门外国语学校2024届高三上学期第二次阶段联考数学试题(已下线)专题3 导数与函数的零点(方程的根)【练】
更新时间:2023-03-16 22:48:00
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解答题-问答题
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【推荐1】已知函数
.
(1)若曲线
在点
处切线方程为
,求
的值;
(2)当
时,函数
有两个不同的极值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2242b6ba2e4fe63dd369204b45a41e.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13653a89d3a38346e1ddf4fd1602f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-证明题
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较难
(0.4)
【推荐2】已知函数
,数列
的第一项
,以后各项按如下方式取定:曲线
在
处的切线与经过
和
两点的直线平行(如图).求证:当
时,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/ea271414-92c1-4b0a-a59a-1b95db2459c3.png?resizew=127)
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba3caa6d08b9d0d090545c118444831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf0462d63993c2b6f61a8c204365b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aab4e235ecd683f59b573d6efd95c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6a9ffffc0c461881b427c543924cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641fec779880f75fa8ee6782f3350402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/ea271414-92c1-4b0a-a59a-1b95db2459c3.png?resizew=127)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71588dadfa3cc42256a2530cef8ab8c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b66621ddd65691649c843f24652d6.png)
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(0.4)
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【推荐3】已知函数
,.
(1)求函数
在点
处的切线方程;
(2)当
时,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85bab33c21ad10bf5cf23852a185ae2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c516ddbd82316cd7a4c0e1e7f599b7.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b0aaf2bb6997da4946b890bd42215d.png)
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较难
(0.4)
【推荐1】已知函数
,
且
,
.
(1)当
时,求曲线
在点
处的切线方程;
(2)设
,
,
,讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24da045dd57e3dc414b340774625890d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb83efe3e960799a86e1fa70b518062c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12f97475d3c67a7629e6d033afa07f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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【推荐2】已知函数
.
(1)若
且仅存在两个整数
,使得
,求
的取值范围;
(2)讨论
零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377d238c69c7c9829280ca67f8bf1bc4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d217c7b12e12e5fb67472452518859ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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较难
(0.4)
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【推荐3】已知
,
.
(1)求方程
的根的个数;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f9c3edab21bca58636372a006d9498.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1da9aa9c7764d416d2b01f78d3e13ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
(1)求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703240220f321f5d3b46395e7db9cd0e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f9c3edab21bca58636372a006d9498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5f58ad9080f2ca1a38fa92ac959c52.png)
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