解题方法
1 . 已知函数
,其中
为常数.
(1)判断
的奇偶性,并说明理由;
(2)若在
上存在![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
个不同的点
(
),满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94eba026ab9188e4deaef4f24f67769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8050bd480227fa5a97d64e74ae97518.png)
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7239984ac3f00112921239e1dd3313c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80be0c3c50d2bd6230b53fbd056122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5867fde790c54e6a931c5d1d22b049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94eba026ab9188e4deaef4f24f67769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8050bd480227fa5a97d64e74ae97518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3dab458f8442e7cf674f6de24ab07c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如果对任意的整数x,y,不等式
恒成立,求最大常数k.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c0252c0000385c3f7bfb989f266c87.png)
您最近一年使用:0次
名校
3 . 已知函数f(x)=|x-1|-2|x+1|的最大值为m.
(1)求m;
(2)若a,b,c∈(0,+∞),a2+2b2+c2=2m,求ab+bc的最大值.
(1)求m;
(2)若a,b,c∈(0,+∞),a2+2b2+c2=2m,求ab+bc的最大值.
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4 . 已知
,函数
,其中
…为自然对数的底数.
(1)证明:函数
在
上有唯一零点;
(2)记
为函数
在
上的零点,证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adb9acead48e36b705874dc96979f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597de8046b5baecf54be4b0516de67ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89e13ea43300cc01379c96614d8e9cc.png)
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2021-10-12更新
|
558次组卷
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3卷引用:湖北省武汉市部分重点中学2021-2022学年高二下学期期末联考数学试题
5 . 已知函数
.
(1)若
,求曲线
在
处的切线方程.
(2)若存在实数
,使得
有两个不同的零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb198cd61088f7a114690dd124b4c902.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/52fcd38273f85e91a1262e95933e6dd4.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82b84d7b00392183ab036460411f09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582d1bd08adeadb5912ce2da715e40d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9d64597e731b6441171c2e2cec21de.png)
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6 . 已知二次函数
有两个不同的零点.若
有四个不同的根
,且
,
,
,
成等差数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0be5afa2a9e64ec663846e1b4c1404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7a9ef0a7eab052019086506c70bd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.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/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
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解题方法
7 . 若函数
在定义域内的某区间
上是严格增函数,而
在区间
上是严格减函数,则称函数
在区间
上是“弱增函数”.
(1)判断
,
在区间
上是否是“弱增函数”(不需证明)?
(2)若
(其中常数
,
)在区间
上是“弱增函数”,求
、
应满足的条件;
(3)已知
(
是常数且
),若存在区间
使得
在区间
上是“弱增函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e82cc461b9607e08a8b31597f6d26df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315b1a62ec3efc43575c57a801ad6585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df515c375a6cd512dafd680a2f8132e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154186900500104502219afe07839158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a29f7f6294171b824722185447384b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2021-12-16更新
|
307次组卷
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3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题
解题方法
8 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c746ae829134912924bd35bd4e39275f.png)
(1)当
时,求函数
的极值;
(2)若存在
,使得
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a274b0623171972513340511781ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c746ae829134912924bd35bd4e39275f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d448e1bab2873fa8e62adb7148a3c197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099adf32792e7334032a80084e0cb584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 对于函数
,若在其定义域内存在 实数x,满足
,则称
为“局部奇函数”.
(1)若
是定义在区间
上的“局部奇函数”,求实数m的取值范围.
(2)若
为定义域R上的“局部奇函数”,求实数n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d88a41a8c39757a1bbcc8ae9052c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1aa1af25a1687ffd40287edd53edc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fac167bab94e9b69db152bd59b86e3f.png)
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2022-11-15更新
|
750次组卷
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6卷引用:河南省焦作市博爱县第一中学2023-2024学年高二上学期9月月考数学试题
河南省焦作市博爱县第一中学2023-2024学年高二上学期9月月考数学试题上海市第二中学2017-2018学年高三上学期10月月考数学试题广东省深圳市高级中学2022-2023学年高一上学期期中数学试题广东省广州市海珠外国语实验中学2022-2023学年高一上学期段考(二)数学试题河南省焦作市博爱县第一中学2023-2024学年高三上学期9月月考数学试题(已下线)第三章 函数的概念与性质(易错必刷40题12种题型专项训练)-【满分全攻略】(人教A版2019必修第一册)
10 . 设函数
.
(1)当
时,求
的最小值;
(2)对任意
,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b2a2849cbe8fd7a61cf36a5069e4a7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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2020-11-28更新
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251次组卷
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5卷引用:浙江省“七彩阳光”新高考研究联盟2020-2021学年高二上学期期中联考数学试题
浙江省“七彩阳光”新高考研究联盟2020-2021学年高二上学期期中联考数学试题2016届浙江省慈溪中学高三上学期期中理科数学试卷(已下线)【新东方】杭州新东方高中数学试卷382(已下线)【新东方】绍兴qw130(已下线)考点60 不等式选讲-备战2021年高考数学(理)一轮复习考点一遍过