1 . 已知函数
,其中
.
(1)函数
在
处的切线与直线
垂直,求实数a的值;
(2)若函数
在定义域上有两个极值点
,
,且
.
①求实数a的取值范围;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04fe3f193e37792ef318de256a7fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aa3adcb154f6144903d456289ecb0f.png)
(2)若函数
![](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求实数a的取值范围;
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c1db4e496877070ca07cc96d568c4a.png)
您最近一年使用:0次
2020-06-15更新
|
3692次组卷
|
5卷引用:山东师范大学附属中学2019-2020学年高二下学期第二次线上检测数学试题
解题方法
2 . 已知函数
,若
恒成立,则实数
的取值范围( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d398df5660bafa31dba5bde5f365cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
3 . 已知函数
.
(Ⅰ)讨论函数
的单调性;
(Ⅱ)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba4be3f799d0433d64a069937ac4b52.png)
(Ⅰ)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅱ)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694ff691286161e389e3638e68dcd12c.png)
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2020-05-25更新
|
320次组卷
|
3卷引用:2020届安徽省池州市高三下学期5月教学质量统一监测数学(文)试题
4 . 已知函数
.
(1)求函数
的单调区间;
(2)当
时,证明:
在
上恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f16c135cafa7e226e56c4af90d842d2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
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解题方法
5 . 如图所示,直角梯形公园
中,
,
,
,公园的左下角阴影部分为以
为圆心,半径为
的
圆面的人工湖,现设计修建一条与圆相切的观光道路
(点
分别在
与
上),
为切点,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/755a866c-22f6-4a94-a861-26e527cf967d.png?resizew=143)
(1)试求观光道路
长度的最大值;
(2)公园计划在道路
的右侧种植草坪,试求草坪
的面积最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ec792fca9dd6dce6078d2cecb223e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbfc4fff61b0627ad494287a6abe456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ab0bd573bfc57dd9444636a04b49a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e4917c34a4c4e654ace35eb65f179b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0079690371546f2f85ba3efc605285a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/755a866c-22f6-4a94-a861-26e527cf967d.png?resizew=143)
(1)试求观光道路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)公园计划在道路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
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6 . 已知函数
,若存在
,使得
,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1473e3b82ca6ada45a0a14bd39413ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee21db6628e4db3f5831370549fa96b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f34d440343370918f1e4d6770bcc2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知函数
.
(1)当
时,求函数
在
处的切线方程;
(2)若函数
在定义域上单调增,求
的取值范围;
(3)若函数
在定义域上不单调,试判定
的零点个数,并给出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c1433f285330a7286c89e6c76a8d09.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
8 . 已知函数
,
.
(1)若函数
的图象与直线
相切,求实数
的值;
(2)设函数
在区间
内有两个极值点
.
(ⅰ)求实数
的取值范围;
(ⅱ)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af636b59b07acdea3f32c324cd9f0068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2dead8f5aa98f35cd681ea18e5eea6.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e88ebfb5c0d6cce558b515be06404d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048e3fa4318163c9980ad5b25985fead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 已知函数
是
上的奇函数(
为常数),
,
.
(1)求实数
的值;
(2)若对任意
,总存在
,使得
成立,求实数
的取值范围;
(3)若不等式
成立,求证实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef48d0c7d50bb70abaf92e31ecc33c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82f36ccbc2c7b8d9bd3aeb7a4cdf123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3a5b4f2b7279a7aa94f8ec12b3f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3afa9b6f5e9873bb4aa72b6473d3f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9f77f71250d5442c74ab2a2778a14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
10 . 如图,已知海岛
与海岸公路
的距离
为
,
,
间的距离为
,从
到
,需先乘船至海岸公路
上的登陆点
,船速为
,再乘汽车至
,车速为
,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/4ee461c5-aa2c-4289-b76a-b07aa62c08a9.png?resizew=151)
(1)用
表示从海岛
到
所用的时间
,并指明
的取值范围;
(2)登陆点
应选在何处,能使从
到
所用的时间最少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6162ce8297482d9ed897a15be5fa2ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5abc4891decbeb113186c62edfe5f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f2ef612f49f4765e46cd9bbb703a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084e821341ae449b597d5d09204d6120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb689a793465929f004e561242fa993.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/4ee461c5-aa2c-4289-b76a-b07aa62c08a9.png?resizew=151)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224a7da7fe6bc28971ce4c277f88588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)登陆点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次