解题方法
1 . 已知函数
.
(1)求
在点
处的切线方程
,并证明
;
(2)若方程
有两个正实数根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ba7f6650a47610941b3ce55b896afe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c887da0c850acf41ab249cc262ae39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdda91b3f668548adb7ea3b66759f99.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca222b41bc1a04389365b9c06ef55008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb94fb3646feaf8ef62e76184c1a2655.png)
您最近一年使用:0次
解题方法
2 . 已知函数
.
(1)若
,求
的图像在
处的切线方程;
(2)若
恰有两个极值点
,
,且
.
①求a的取值范围;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1091ad3396a0b24d1055592871faf379.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.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/26d8dafc71b106f39f4e15442220897b.png)
①求a的取值范围;
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bd8942073cbb431bb850bf81bb8c89.png)
您最近一年使用:0次
解题方法
3 . 已知
.
(1)当
,证明
;
(2)讨论
的单调性;
(3)利用(1)中的结论,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebc745a5447d68aa4d43aaff2614a42.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)利用(1)中的结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450940c16da05563afa896f50ac33332.png)
您最近一年使用:0次
4 . 已知函数
,
,
在
上有且仅有一个零点
.
(1)求
的取值范围;
(2)证明:若
,则
在
上有且仅有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c4d0b1cf4cae0756fc05e1695dc813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406b668b14dbdd75ad591fa8d5fa4b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf9befc3b336d83b83bcfcbc19c0752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e601d5f49a28dd69ed4e6fa1bab251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4a7c40492ac55e2b593a7dec23248a.png)
您最近一年使用:0次
2022-11-01更新
|
484次组卷
|
3卷引用:山西省临汾市等联考2023届高三上学期期中数学试题
解题方法
5 . 已知函数
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
(1)当
时,证明![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439768d3a276ea91142b455df8f2a55a.png)
(2)若存在实数b,使得
在
上恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6bdb5c0ddd5e123da5027486460b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439768d3a276ea91142b455df8f2a55a.png)
(2)若存在实数b,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84dec7f92258cdc52b6653a0fe129cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a20570016dcade92a03583ca7a74a8.png)
您最近一年使用:0次
2022-02-15更新
|
479次组卷
|
2卷引用:山西省临汾市2022届高三高考考前适应性训练(一)数学(理)试题
名校
解题方法
6 . 已知函数
,
的图象在点
处的切线为
.
(1)求函数
的解析式;
(2)设
,求证:
;
(3)若
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f759792028843084024c269f5355429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d4f20f4d98141613ff5dd7c37b55c3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a0b5bb152443fe850a9db6bf4f7d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0879734ee766cb630cfeb3f25fea7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8467418380f4b7faa6c7955084db81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-06-23更新
|
554次组卷
|
18卷引用:山西省临汾市洪洞县第一中学2020届高三上学期期中数学(文)试题
山西省临汾市洪洞县第一中学2020届高三上学期期中数学(文)试题河北省衡水中学2017届高三高考押题卷三卷理数试题2019届高考数学人教A版理科第一轮复习单元测试题:第三章 导数及其应用河北省衡水中学2018年高考押题(三)理科数学【全国百强校】宁夏银川一中2019届高三第三次月考数学(文)试题【校级联考】福建福鼎三校联考2019届高三上半期考文科数学试题安徽省淮北市淮北师范大学附属实验中学2018-2019学年高二下学期第二次月考数学(理)试题(已下线)2020届高三12月第02期(考点03)(文科)-《新题速递·数学》河北省唐山市玉田县2018-2019学年高二下学期期中数学(理)试题河北省唐山市玉田县2018-2019学年高二下学期期中数学(文)试题广东省顺德区容山中学2019-2020学年高二下学期期中数学试题四川省成都市青白江区南开为明学校2019-2020学年高二下学期第三次月考数学(文)试卷浙江省宁波市奉化高中、慈溪市三山高中等六校2019-2020学年高二下学期期中联考数学试题江苏省淮安地区五校2019-2020学年高二下学期6月联考数学试题西藏自治区日喀则区南木林高级中学2021届高三上学期第二次月考数学试题江苏省南通市海门市包场高级中学2020-2021学年高二上学期期中数学试题江西省萍乡市芦溪中学2023届高三上学期开学考数学(文)试题福建省福州市第四十中学2022-2023学年高二下学期期末阶段练习数学试题
7 . 已知函数
.
(1)讨论
的单调性;
(2)设
,
,
,
是曲线
上任意三点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ae3a06e2db61ce958f143eb7f7390b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c06ceee2b1e227de025476eee95672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aec64971ce081682c67ad33b4fad90a.png)
您最近一年使用:0次
解题方法
8 . 设函数
.
(1)当
时
恒成立,求k的最大值;
(2)证明:对任意正整数n,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395e5476bfffe1f1ddad97dfaa8023e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)证明:对任意正整数n,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a75a66bf80f27de1aff69034048d45.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)若
在
处的切线与直线
垂直,求
的极值;
(2)若函数
的图象恒在直线
的下方.
①求实数
的取值范围;
②求证:对任意正整数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5d7bf46fe9b64f762ebcd347d155fb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957446b2f02eeaf2a1e29794036f1131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②求证:对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ba7d30c23e7ff46853402a9a8a0334.png)
您最近一年使用:0次
2020-03-18更新
|
345次组卷
|
2卷引用:山西省临汾市2020届高三下学期模拟考试(2)数学(理)试题
解题方法
10 . 设曲线
在
处的切线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fe3ffe16ce7afd33bddb4c9d161fec.png)
(1)求a,b的值;
(2)求证:
有唯一极大值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a77fd83906b87b88a90c5814e9e9a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068ff25c767fcbe6fe596d996031eed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fe3ffe16ce7afd33bddb4c9d161fec.png)
(1)求a,b的值;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe206a3088aff8fe04d8b65a66786372.png)
您最近一年使用:0次