名校
1 . 关于
的函数
,我们曾在必修一中学习过“二分法”求其零点近似值.现结合导函数,介绍另一种求零点近似值的方法——“牛顿切线法”.
(1)证明:
有唯一零点
,且
;
(2)现在,我们任取
(1,a)开始,实施如下步骤:
在
处作曲线
的切线,交
轴于点
;
在
处作曲线
的切线,交
轴于点
;
……
在
处作曲线
的切线,交
轴于点
;
可以得到一个数列
,它的各项都是
不同程度的零点近似值.
(i)设
,求
的解析式(用
表示
);
(ii)证明:当
,总有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3904b79fdb74189b8b9933fdb6b341.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beecc7a1e5d079e0bcde356848626436.png)
(2)现在,我们任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8f08fa7920ab3d6b3ec6c831a43fe3.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb652143b43cc9439a347b2b1dc5cf6.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc47735cc385a3474bc1dabad322304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367304824e7eb354ffeb937fa209d80d.png)
……
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641fec779880f75fa8ee6782f3350402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbac61ee33f7cbd19ffe10582e8f1f6.png)
可以得到一个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(i)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c0a98e6d574ec3702340e64bba6c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091f2176a35c27ac4bdddcda85de5bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ee4b6d8f24ec689324efbf66a52e80.png)
(ii)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449f1600850683d2ac445d97e7a3b5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a415b86943618bf0c8ebc5951a1aef.png)
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|
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解题方法
2 . 已知双曲线
的左、右焦点分别为
,
,点
是
右支上一点,若I为
的内心,且
.
(1)求
的方程;
(2)点A是
在第一象限的渐近线上的一点,且
轴,
在点P处的切线l与直线
相交于点M,与直线
相交于点N.证明:无论点P怎么变动,总有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd892f1eec174b7ddf68146514b758b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6dc791ae552024ea0df7905bf190f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace7c9e3da8613175ca07c54c116127a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d1611e780839e2ff7cf52c46a31b68.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)点A是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dc06fe67c281c3ad3d19d6d8c98a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ac1f3d675f528be8fd22ea2ac6fb4c.png)
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解题方法
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadd3d747cc83991a9f9022007c4718.png)
(1)若
在
处的切线方程为
,
(i)求a,b的值;
(ii)讨论
的单调性.
(2)若
,证明:
有唯一的极小值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfadd3d747cc83991a9f9022007c4718.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(i)求a,b的值;
(ii)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d00e896ece0bec6845cdf25235bcbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
4 . 已知函数
.
(1)当
时,求函数
的图象在
处的切线方程.
(2)若函数
在定义域上为单调递增函数.
①求整数
的最大值;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5807f807737f3a31a849f0ccc60f33.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dfb495fb337b2c28b84e2a6c9385d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①求整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773d5a5be51017b4b06f4a4d572dd6aa.png)
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2021-10-08更新
|
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3卷引用:福建省莆田第一中学2022届高三上学期期中考试数学试题
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5172023b6b94d8f9d928a0ba507a5647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6999cc41d0de41c4114f4adda1952ca.png)
(Ⅰ)若
,求曲线
在
处的切线方程;
(Ⅱ)若
存在极小值点
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5172023b6b94d8f9d928a0ba507a5647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6999cc41d0de41c4114f4adda1952ca.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff7fd582c11b27f3d4da4e54e2f7d7b.png)
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名校
6 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)讨论
的单调性;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8612cb98d1d13a2074cc07a401f0fa5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187a3919ec9b72b0261d63db76b207e5.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c84b49231d0344d0813a7bbd2acdaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2476a9263daa27029a2d26cc0ba373.png)
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2021-08-08更新
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3卷引用:福建省龙岩市永定区坎市中学2023届高三上学期期中数学试题
福建省龙岩市永定区坎市中学2023届高三上学期期中数学试题重庆市第八中学2020-2021学年高二下学期第二次月考数学试题(已下线)专题01 《导数及其应用》中的典型题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
名校
7 . 已知函数
,曲线
在点
处的切线方程为
.
(1)求实数
的值,并证明:对
,
恒成立.
(2)设函数
,试判断函数
在
上零点的个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e643a973cc6912a32b96d1893e54ac.png)
![](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/0985b973395bcd371cd1e26d3fcd1c36.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96cc2abd23e9e9b92fbf52bc335a5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e601d5f49a28dd69ed4e6fa1bab251.png)
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福建省连城县第一中学2022-2023学年高二下学期3月月考数学试题辽宁省朝阳市2021届高三一模数学试题重庆市酉阳土家族苗族自治县第三中学校2021届高三数学考前猜题卷试题(已下线)专题4.13—导数大题(零点个数问题2)-2022届高三数学一轮复习精讲精练(已下线)预测10 导数的综合应用-【临门一脚】2021年高考数学(理)三轮冲刺过关(已下线)预测10 导数的综合应用-【临门一脚】2021年高考数学(文)三轮冲刺过关甘肃省武威市武威六中2020-2021学年高三第十次诊断考试数学(理)试题陕西省渭南市瑞泉中学2022-2023学年高三上学期第二次教学质量检测理科数学试题
名校
解题方法
8 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若函数
存在三个零点,分别记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
.
(ⅰ)求
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5601a7395737194a6e241ac337abbb5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915e28a6131cf12ea62c8f469d4fa5f2.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
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2021-03-27更新
|
1296次组卷
|
5卷引用:福建省福州市福清西山学校2022-2023学年高二下学期5月月考数学试题
福建省福州市福清西山学校2022-2023学年高二下学期5月月考数学试题北京市丰台区2021届高三一模数学试题山东省济宁市任城区2020-2021学年高二下学期期中考试数学试题宁夏青铜峡市高级中学2022届高三上学期期中考试数学(理)试题(已下线)高二数学下学期期中全真模拟卷(1)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(原卷版)
9 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)讨论
的单调性;
(3)当
时,证明不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aecb0d628de6f9c5982bba2d4693115a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3915bbb296ffc89ba0de46989ad0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134fdd9d6a725445b21879b8af4a73dd.png)
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解题方法
10 . 已知函数
.
(1)若曲线
存在一条切线与直线
垂直,求a的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829b174ab8930e4c74d016d2f0dab374.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1447dbe580ac5c825776995118e75acf.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5092471545ae8a63c485099da81b0524.png)
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2020-12-14更新
|
530次组卷
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7卷引用:福建省莆田市2021届高三高中毕业班第一次教学质量检测数学试题
福建省莆田市2021届高三高中毕业班第一次教学质量检测数学试题湖北省恩施州2020-2021学年高三上学期第一次教学质量监测考试数学试题陕西省部分重点高中2020-2021学年高三上学期12月联考理科数学试题河北省2021届高三上学期12月月考数学试题云贵川桂四省2020-2021学年高三上学期12月联合考试数学理科数学试题(已下线)专题09 导数压轴解答题(证明类)-1(已下线)专题9 利用放缩法证明不等式【讲】