10-11高三·河南新乡·阶段练习
解题方法
1 . 已知定义在R上的函数
的图象关于原点对称,且
时,
取得极小值
.
(1)求
的解析式;
(2)当
时,函数图象上是否存在两点,使得过此两点处的切线互相垂直?证明你的结论;
(3)设
时,求证:|
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85042fe1d1a07cee1f19080c0dac2ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7eb3b5ab19d97f6c7df36294ccc3674.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dca32eacf771f7949345ae9a2764a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9de2cc3c734277b52365231731675c.png)
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2013·江西南昌·二模
2 . 理科已知函数
,当
时,函数
取得极大值.
(Ⅰ)求实数
的值;(Ⅱ)已知结论:若函数
在区间
内导数都存在,且
,则存在
,使得
.试用这个结论证明:若
,函数
,则对任意
,都有
;(Ⅲ)已知正数
满足
求证:当
,
时,对任意大于
,且互不相等的实数
,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0506b5763f06f6ae9dfa8c6d104a1c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0506b5763f06f6ae9dfa8c6d104a1c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68a1147fd7289d45ecd47bb0b42707d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f649784a05e98b05dac141227c72e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0588ae41d01b164bf1aaffeadad2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a718ce8b0d35d734c1f21248d925b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a133c5814447729d4065414d8cb0fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/741c9f67009ffda2bab297ba3e4fb4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7856ee6dd4ec9d77d24e2c138fd4ec.png)
![](https://img.xkw.com/dksih/QBM/2013/5/7/1571205295046656/1571205301100544/STEM/2acebd3106434e11886e5565d26732ff.png)
![](https://img.xkw.com/dksih/QBM/2013/5/7/1571205295046656/1571205301100544/STEM/6dbee9eb63824c0bbeb211f8e65031e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece1cabeedc0da3de06bd8b7753cdf52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aeb9164a010e37929d910a08523e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf1f029bb36d7d199ed2b782490c424.png)
![](https://img.xkw.com/dksih/QBM/2013/5/7/1571205295046656/1571205301100544/STEM/ea87558e0c74427ba4ed0e0bb16c5170.png)
![](https://img.xkw.com/dksih/QBM/2013/5/7/1571205295046656/1571205301100544/STEM/8f9efb8e96184b5083a84185fb7866c2.png)
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2024·全国·模拟预测
解题方法
3 . 已知函数
.
(1)若
的极值为-2,求a的值;
(2)若m,n是
的两个不同的零点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea466497de817df90ba841113536b9d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若m,n是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e815aee0e765e618a519eb59bfba32a1.png)
您最近一年使用:0次
2024·全国·模拟预测
4 . 已知函数
.
(1)若曲线
在
处的切线方程为
,求
的值及
的单调区间.
(2)若
的极大值为
,求
的取值范围.
(3)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfa6a78ae556815247efd81e5764e12.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26f06d62dfc4005bc88f82dd4445af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f962599efd96d96dac91c38574f21a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd7ad42edb14d2a23ca3eb74139e036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b25f35313906891521cd848ed4a95e.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
,
.
(1)求证:
,
恒成立;
(2)若
存在极值,求a的取值范围;
(3)若
时,
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410b9ca67a305a4b48e8a56ef23ec558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84a145ca995d46f2e8f09af8a78930a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e396ac92f3b89e7c8afe1799b24114e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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6 . 设函数
,
有唯一极值点
.
(1)证明:
;
(2)若
,求
的取值范围;
(3)若
的图象上不存在关于直线
对称的两点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be31d79dcf1ba2248c8fd8532e2e727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2367b48e8f6dbbfe3dd14f6eab8238a5.png)
![](https://img.xkw.com/dksih/QBM/2024/3/28/3463519110799360/3467824765468672/STEM/4236e158880542c4b9d3318290fe1b8b.png?resizew=8)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529aaddc617f821a66bfffb1a41303ab.png)
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2024·全国·模拟预测
解题方法
7 . 已知函数
在区间
上存在两个极值点
,
.
(1)求实数a的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a09ba7ec2175294da7df6c6913ce4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360598a0e76d28c618fe3573bfe5f85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)求实数a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6d9f798a99a7b28888820716549f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59b428e2eef55e7aa259ab433750670.png)
您最近一年使用:0次
8 . 已知函数
.
(1)若
,求证:
;
(2)若函数
在
处取得极大值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ffae39f71fe2bebfa87fd627a808b5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-11-24更新
|
331次组卷
|
3卷引用:湖北省宜昌市协作体2023-2024学年高三上学期期中考试数学试题
9 . 已知函数
.
(1)若
存在极值,求
的取值范围;
(2)若
,已知方程
有两个不同的实根
,
,证明:
.(其中
是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a472d59860950f04f692170fc3ed557.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde6a3019187bddf6f394cfb76f6f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc1a451a2c80b297f3d71d8beaf54be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
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2023-09-16更新
|
732次组卷
|
3卷引用:湖南省长沙市周南中学2023-2024学年高三上学期第二次阶段性测试数学试题
湖南省长沙市周南中学2023-2024学年高三上学期第二次阶段性测试数学试题(已下线)考点19 导数的应用--函数零点问题 2024届高考数学考点总动员【练】广东省佛山市2024届高三上学期教育教学质量检测模拟(二)数学试题
解题方法
10 . 已知函数
,
.
(1)若
的极大值为1,求实数a的值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c013a7b9d9eba700eb2c7dca0e9e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d70521231eeb9f0c3f58412c08b3f1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
您最近一年使用:0次
2023-12-14更新
|
2076次组卷
|
11卷引用:2024年全国高考名校名师联席命制型数学信息卷(四)
(已下线)2024年全国高考名校名师联席命制型数学信息卷(四)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(七)(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(七)湖北省新洲区部分学校2024届高三上学期期末数学试题湖南省“一起考”大联考2023-2024学年高三下学期模拟考试数学试题(一)湖南省衡阳市衡阳县第二中学2023-2024学年高二上学期期末达标测试数学试题(A卷)(已下线)第04讲 导数在研究函数中的应用-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(已下线)第10讲:导数期末题型突破(单调性、不等式、零点、恒成立)(已下线)专题4 导数在不等式中的应用(讲)(已下线)模块一 专题6 导数在不等式中的应用(讲)(人教B版)(已下线)模块一 专题4 《导数在不等式中的应用》(苏教版)