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1 . 已知函数
,且正数a,b满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45e3adfad77798d50f3cc64920fab44.png)
(1)讨论f(x)的单调性;
(2)若
的零点为
,
,且m,n满足
,求证:
.(其中
……是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06e634430688fb60f1534d658f4379b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45e3adfad77798d50f3cc64920fab44.png)
(1)讨论f(x)的单调性;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60699e3e7a4c73c8a5e4585013e4da6.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/0288311544d306cfa4b9e56ae707eeff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f145ad1f0a2e33f6d0cb48ea4caefba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
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2 . 下列不等式正确的有( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 已知数列
和
,
且
,函数
,其中
.
(1)求函数
的单调区间;
(2)若数列
各项均为正整数,且对任意的
都有
.求证:
(ⅰ)
;
(ⅱ)
,其中
为自然对数的底数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee03c109e4f64f3539de74ef30f06fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc65a38fceb3231eada88b96f0c63d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b0b716fda9b1efd9e47e2d80543f2d.png)
(ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf779c918958c14824cd7d952a4bb4bc.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462a81927ad910cd66ae9a5fd5813502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
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2022-04-07更新
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3卷引用:安徽省滁州市2022届高三下学期第二次教学质量检测理科数学试题
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4 . 对于数列
,若存在正数
,使得对一切正整数
,恒有
,则称数列
有界;若这样的正数
不存在,则称数列
无界,已知数列
满足:
,
,记数列
的前
项和为
,数列
的前
项和为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088726808d684616b8e79c495bc9e591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a45db5d8a0994225fba569e9963d7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
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6卷引用:浙江省温州市2022届高三下学期3月高考适应性测试数学试题
浙江省温州市2022届高三下学期3月高考适应性测试数学试题(已下线)专题12 数列(已下线)第5章 一元函数的导数及其应用 单元综合检测(难点)(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-1上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题(已下线)【练】专题4 数列新定义问题
2022高三·全国·专题练习
解题方法
5 . 定义:若
在
上为增函数,则称
为“
次比增函数”,其中
,已知
.(其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98aee93d3cea0c63fcde63c9a5f3390.png)
(1)若
是“1次比增函数”,求实数
的取值范围;
(2)当
时,求函数
在
上的最小值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3fbc772974d02975aa4ba349fcf234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf65f424a8cfccb01cd9cf90f74e863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28296681cf270d1db6103d5c69f97d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98aee93d3cea0c63fcde63c9a5f3390.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6e28dbfcdd6fb66b9ff759be044287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba40f7e34a93534bd8b9c789e280f25b.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5516279ed943f5e7eed3d8156ebcf46.png)
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6 . 已知函数
(e为自然对数的底数).
(1)求证:
时,
;
(2)设
的解为
(
,2,…),
.
①当
时,求
的取值范围;
②判断是否存在
,使得
成立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abd52a21627a3233cd377aa1a257189.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8a82d291105594bb2f97fb81b165d0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2e727ac09acdaafb6c97e4f5c50aa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803092f422dcd99c23e821770b923188.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2daf2bf93c9c6fceee6b8068ee19d111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9727721cbac7d8d47c511fe934f9215d.png)
②判断是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2498a2158280a2502d58ccfc84e5bc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2bed16e997a85f5d6d1a4d2d89a83f.png)
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2021·全国·模拟预测
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7 . 已知函数
(
)有两个不同的极值点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8923affba77d55b330a58dd208d84b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
A.若![]() ![]() ![]() |
B.函数![]() ![]() |
C.实数a的取值范围为![]() |
D.若函数![]() ![]() ![]() |
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8 . 若直线
与两曲线
分别交于
两点,且曲线
在
点处的切线为
,曲线
在
点处的切线为
,则下列结论:
①
,使
;②当
时,
取得最小值;
③
的最小值为2;④
.
其中所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26c7605338f5766155296b13cf99147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d115cf2f2e63304d4f31946db866de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14efb0184968017766c8f60cf6fc31a1.png)
其中所有正确结论的序号是( )
A.① | B.①②③ |
C.①②④ | D.①②③④ |
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2021-12-04更新
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6卷引用:四川省宜宾市普通高中2022届高三上学期第一次诊断测试理科数学试题
四川省宜宾市普通高中2022届高三上学期第一次诊断测试理科数学试题(已下线)专题3-5 超难压轴小题:导数和函数归类(2)-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)江西省宜春市上高二中2022届高三5月第十次月考数学(理)试题(已下线)第07讲 利用导数研究函数的单调性(核心考点讲与练)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)江西省抚州市临川第一中学2021-2022高二12月月考数学(文)试题(已下线)专题08 导数与函数综合压轴(选填题)-2
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9 . 对于定义在D上的函数
,其导函数为
.若存在
,使得
,且
是函数
的极值点,则称函数
为“极致k函数”.
(1)设函数
,其中
,
.
①若
是单调函数,求实数a的取值范围;
②证明:函数
不是“极致0函数”.
(2)对任意
,证明:函数
是“极致0函数”.
![](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/c7807143d8a2929459b46063519843f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0da9fd5dfe735b958eb002702baa2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48196cf98394fcbce4181c33754141dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375a66a688f4a9133fde13d212901c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bffdee54569b89c743b86a90f28b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc26fdf6289ac213b712cc32619e1e2.png)
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2021-11-04更新
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5卷引用:上海市建平中学2021-2022学年高二下学期期末数学试题
上海市建平中学2021-2022学年高二下学期期末数学试题北师大版(2019) 选修第二册 突围者 第二章 第六节 课时2 函数的极值(已下线)重难点04导数的应用六种解法(2)辽宁省部分学校2024届高三上学期期末数学试题(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)
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10 . 设函数
.
(1)证明函数
在
上是递减函数,在
上是递增函数;
(2)函数
,若实数
,满足
,求
的最小值;
(3)函数
如(2)中所述,
是定义在
上的函数,当
时,
,且对任意的
,都有
成立,若存在实数
满足
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad088956aa34f0f709914dc8a2d9263.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6e01f72f4ad539e048680eb2a7a9d2.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d150a76e9bac9ead375e43f0784249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e859c3fea2978dffe91deb3fef54eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f417f76e2e7eb5231d8e90fb85c5b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362c09f673017d42b868689cdd1c52e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62077399a91d53169335549714e166a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2d4d7ccd61172d021423109eba962f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f6a3b0fe36c8b8d982cac77a79c23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ddda93ac287ebe35a48b644cbc5e3a.png)
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