名校
1 . 已知
,函数
.
(1)当
时,求
的单调区间;
(2)当
时,设
的导函数为
,若
恒成立,求证:存在
,使得
;
(3)设
,若存在
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fef330410912ad36677dbf8549b7f7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0953444691256f713639f4ded91ff306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990ea00761500cbd2a51283a2f443421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c72d250a079379c5175693c165248c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f8f8ab529ff605ee0c00e551a01622.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ae80746de8e491dcb8df4b1c42dbea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478052f005a72e660f55b439e77955dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c247baa451cd7868d97daa7103085ae.png)
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2024-06-11更新
|
239次组卷
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5卷引用:新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题
新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题天津市部分区2023届高三二模数学试题(已下线)第九章 导数与三角函数的联袂 专题三 含三角函数的恒成立问题 微点3 三角函数的恒成立问题(三)(已下线)专题6 导数与零点偏移【练】(已下线)2024年天津高考数学真题平行卷(提升)
2 . 已知函数
.
(1)证明曲线
在
处的切线过原点;
(2)讨论
的单调性;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47dd2852e029e5b030f26a5ad0543bb.png)
(1)证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68cb9f9f7935fd5703f46181db6e4db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-04更新
|
2308次组卷
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5卷引用:新疆维吾尔自治区乌鲁木齐市2024届高三第一次质量监测数学试题
解题方法
3 . 在平面直角坐标系
中,重新定义两点
之间的“距离”为
,我们把到两定点
的“距离”之和为常数
的点的轨迹叫“椭圆”.
(1)求“椭圆”的方程;
(2)根据“椭圆”的方程,研究“椭圆”的范围、对称性,并说明理由;
(3)设
,作出“椭圆”的图形,设此“椭圆”的外接椭圆为
的左顶点为
,过
作直线交
于
两点,
的外心为
,求证:直线
与
的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9859b2a9747b7a9da0b87624231e5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de32f743ea0cf45f9822dd603be212d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd95e24f73f48167eb193951bd4fa7fb.png)
(1)求“椭圆”的方程;
(2)根据“椭圆”的方程,研究“椭圆”的范围、对称性,并说明理由;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715c3978c454777672e14a72298317a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dd7df0a96857b265fbbf745873ace9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-03-22更新
|
939次组卷
|
3卷引用:新疆乌鲁木齐地区2024届高三第二次质量监测数学试题
解题方法
4 . 已知函数
,
.
(1)求
的极值;
(2)证明:当
时,
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923fcc6830f02925f594edcb9fcc90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bcf1135449e1c9bb97f6927aa55b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cd1568daf759620e6842d75d88d558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
您最近一年使用:0次
2023-09-19更新
|
403次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市第六十一中学2024届高三上学期10月月考数学试题
名校
5 . 已知
,设函数
,
是
的导函数.
(1)若
,求曲线
在点
处的切线方程;
(2)若
在区间
上存在两个不同的零点
,
.
①求实数
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5156fa5305e2cff005eda383602fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6bd2647b0eebe283a787884498641f.png)
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2023-05-14更新
|
1057次组卷
|
7卷引用:新疆生产建设兵团第三师图木舒克市第一中学2024届高三上学期11月月考数学试题
新疆生产建设兵团第三师图木舒克市第一中学2024届高三上学期11月月考数学试题湖北省襄阳市第四中学2023届高三下学期5月适应性考试(二)数学试题福建省厦门双十中学2023届高三热身考试数学试题(已下线)专题19 导数综合-2河南省郑州市宇华实验学校2024届高三上学期期末数学试题(已下线)专题3 导数与函数的零点(方程的根)【讲】(已下线)专题8 导数与拐点偏移【讲】
6 . 已知函数
,
.
(1)讨论
的单调性;
(2)若方程
有两个不相等的实根
,求实数
的取值范围,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0475176098f9b774e0a9e3ede4ada3d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6e28dbfcdd6fb66b9ff759be044287.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81861bdb48b1df503c6550dbff5923c5.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/ab825645822c950a11ffabcaabb29df0.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,其中
为常数.
(1)设
为
的导函数,当
时,求函数
的极值;
(2)设点
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
,曲线
在点
处的切线的斜率分别为
,直线
的斜率为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edceb1f45633fa5111f9d7fe05177fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47fe863357e026cd960fea54a3ac827d.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b205b99f0e7332c9646d926c8ab226c8.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4e42cab981d3a73d1a1562ea03c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4ca086fca586da964c007788de45cc.png)
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2022-03-21更新
|
837次组卷
|
4卷引用:新疆维吾尔自治区乌鲁木齐市第十一中学2024届高三上学期12月月考数学试题
8 . 已知函数
.
(1)若函数
在
处的切线与直线
垂直,求
的值;
(2)若
存在三个极值点
,
,
,且
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029adeae29984672ec6bbbc9189a21a1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cc9d97a3f95840ca9955bcdc4df529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710755df750ad00f0ae2b81f528d6595.png)
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2022-03-26更新
|
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|
2卷引用:新疆乌鲁木齐地区2022届高三第二次质量监测数学(理)试题(问卷)
解题方法
9 . 已知函数
.
(1)试比较
与
的大小.
(2)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7122cad07fd1ccd17205a6f213c42ddf.png)
(1)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b5a9de8a72dda70e3eefeb0a408ffd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
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2022-03-26更新
|
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5卷引用:新疆昌吉学联体2022届高三下学期第三次高考适应性联考数学(文)试题
新疆昌吉学联体2022届高三下学期第三次高考适应性联考数学(文)试题河南省平顶山市汝州市2022届高三3月联考文科数学试题(已下线)第13讲 拓展六:泰勒展开式与超越不等式在导数中的应用(讲)-2023年高考数学一轮复习讲练测(新教材新高考)(已下线)第二篇 函数与导数专题4 不等式 微点9 泰勒展开式(已下线)专题11 利用泰勒展开式证明不等式【练】
名校
10 . 已知函数
.
(1)当
时:
①解关于
的不等式
;
②证明:
;
(2)若函数
恰有三个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca766a161f9438aef446b1beb7de3c4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
①解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d80a96345f600468f0efb316ccd586.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1048afd2ea59732a2119a2863ed77b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-01-11更新
|
1233次组卷
|
4卷引用:新疆维吾尔自治区疏勒县2022届高三第一次调研测试数学试题