解题方法
1 . 设函数
,
,
.
(1)若
,
,求
的最值;
(2)若
及
,总有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41afa6d6f2b5168114ef658a6e7335fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4633de9335d15d7685bdecb007a3678c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8e1dd8da540badcb9a8f427c5b202e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1f0004bc2fb1434294fc7dd7e935d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dd4a322f8ccc998de9edc3d72fe86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e876fd3740563a9b1ac064bb190333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95895ef562575bcdd3060e8549b36017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
2 . 已知函数
,在点
处的切线为
.
(1)求
,
的值及函数
的单调区间;
(2)若
,
是函数
的两个极值点,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c3243e8eed9b404423f81a627f85f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/99b5403b296ab61d53dd176e2c3e7349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13e5c66b641e6f5bfddff5d1997a34.png)
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2020-10-08更新
|
485次组卷
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2卷引用:重庆市西南大学附属中学2021届高三上学期第一次月考数学试题
名校
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65887c0436c24ead8eb6eb9b5698359b.png)
(1)
时,求函数
的极值;
(2)
时,讨论函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65887c0436c24ead8eb6eb9b5698359b.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2020-09-13更新
|
309次组卷
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2卷引用:云南民族大学附属中学2020届高三第一次高考仿真模拟数学(理)试题
解题方法
4 . 已知
.
(1)证明:
;
(2)对任意
,
,求整数
的最大值.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6068e5fccbb144797b212bc8b9a6f7a2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1136ca42f76bcb8ecbec5cf2c29b6121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b596e3c50904ae44375647f0f322d2b.png)
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5 . 已知函数
(其中
,且
),
是函数
的导函数,设
.
(1)当
时,求函数
的单调区间;
(2)若函数
在
上存在唯一的零点
,求
的值.(其中
表示不超过x的最大整数,如
,
,
.)
参考数据:
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0f6ce702a1c6e04a97615f57fd69b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e332244bb656f81672266b5b61e304.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a25ffcd4f2175085e6c93176cb10d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46d26318d841b23b93a236816abfae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069168253cb54985671be43e60a5ff85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddad22a83712f4bd0f19c73049dd096.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b7cfcc147916ae7eeb5d557fea945e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25522700e456c259978a6d762e818572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d90807e6a0085068ae47a101b7c87d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db954dea085e42d5266652072a5c67c.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
,
,
,且
的最小值为0.
(1)若
的极大值为
,求
的单调减区间;
(2)若
,
的是
的两个极值点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd125568cf7100a22c4ec73698f7474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90e8d5d7fed033f48270b1ff825fcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8806602a7954aa6a067d8c6aed8e239f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2349e3509799b01ce88ce91a0d7dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c72cdf3b7f15f2b775e80ac15de403.png)
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2020-06-15更新
|
3800次组卷
|
4卷引用:云南省昆明市第一中学2020届高三考前第九次适应性训练数学(理)试题
云南省昆明市第一中学2020届高三考前第九次适应性训练数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)极值点偏移专题08极值点偏移的终极套路新疆维吾尔自治区乌鲁木齐市第四十中学2024届高三上学期11月月考数学试题
7 . 已知函数
.
(1)讨论
的单调性;
(2)证明:
.注:
为自然对数的底数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068132ef9604287c220c731012efec01.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f2df1570205c3018e8562cce8a3f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
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2020-05-22更新
|
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3卷引用:云南省玉溪市2019-2020学年高三第二次教学质量检测数学(理)试题
云南省玉溪市2019-2020学年高三第二次教学质量检测数学(理)试题江西省赣州市十五县(市)2019-2020学年高二下学期期中联考数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)
名校
解题方法
8 . 已知函数
,
.
(1)当
时,设函数
在区间
上的最小值为
,求
;
(2)设
,若函数
有两个极值点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a35c267862c082fbdd4e6dce769de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83eb829e3338a9e4be598124855685e8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812b1efe6b4a2c6cdabfaf0d903bfecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f252477a0de25fb08083c50b12b9fbb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6dce404b0bd7671b522eb99ca71f76.png)
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2020-04-21更新
|
712次组卷
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5卷引用:2020届百师联盟高三练习题(一)(全国卷 II)数学(理)试题
9 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,判断并说明函数
的零点个数.若函数
所有零点均在区间
内,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f73aadd820228b7b05feb4227c9a01.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4011e35096d99aadacd2d7d87e7bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae3668b00ba85b12cbcfcdf3631cf92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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2020-04-08更新
|
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4卷引用:云南师范大学附属中学2019-2020学年高三高考适应性月考(六)数学(理)试题
云南师范大学附属中学2019-2020学年高三高考适应性月考(六)数学(理)试题云师大附中2019-2020学年高三高考适应性月考(六)数学(理)试题四川省乐山市2020届高三第三次调查研究考试数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)
名校
10 . 已知函数
.
(1)若
,求函数
的单调区间;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5921959f23290c17c6315d11267ac6d6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-03-27更新
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2卷引用:2019届浙江省高三下学期4月高考模拟测试数学试题