名校
1 . 已知函数f(x)=a-
-lnx,g(x)=ex-ex+1.
(1)若a=2,求函数f(x)在点(1,f(1))处的切线方程;
(2)若f(x)=0恰有一个解,求a的值;
(3)若g(x)≥f(x)恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf35027e76f8ea593f82023973d4aba3.png)
(1)若a=2,求函数f(x)在点(1,f(1))处的切线方程;
(2)若f(x)=0恰有一个解,求a的值;
(3)若g(x)≥f(x)恒成立,求实数a的取值范围.
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df2cf24698766c54e7a7c61d4ad2bfb.png)
(1)当
时,求函数
的单调区间;
(2)若方程
在区间
上有实数解,求实数a的取值范围;
(3)若存在实数
,且
,使得
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df2cf24698766c54e7a7c61d4ad2bfb.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac0a38f359dd17a73c3e9f7bbbc5be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e15f0b1bdff81fe56227d1141f8bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87027136ff548fc504dea240e75cea86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc9edb22a22dd339bf9f169e6642169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe357c4d3077bdf6f6f88921a234bc1.png)
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3 . 已知函数
在
处的切线的斜率为1.
(1)如果常数
,求函数
在区间
上的最大值;
(2)对于
,如果方程
在
上有且只有一个解,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83eefc0aaac0612825479ae5b59dc4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(1)如果常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402ff24c742e538e4a13f88fa86e5945.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b87e91acd8d9f8ff96a347070a0ef99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
4 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569ff6208a1c81a3bfba3f59fae3a8e5.png)
(1)当
时,求函数
的单调区间;
(2)令
,其图象上任意一点
处切线的斜率
恒成立,求实数
的取值范围.
(3)当
时,方程
在区间
内有唯一实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569ff6208a1c81a3bfba3f59fae3a8e5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa3dc4e22ccb7a22bc255aa53a4881b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3348348fffffca829e5cce19d50b0126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fbbb9c4b0f7937c003ef2c218c02a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0953444691256f713639f4ded91ff306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c34d2e40ee0263ecd6b6737c47bf98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ff8b9bb03914903419312ec8150a32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 设函数
.
(1)当
时,函数
取得极值,求
的值;
(2)当
时,求函数
在区间
的最大值;
(3)当
时,关于
的方程
有唯一实数解,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca40a79d934b5208e0f0fd8aa39aa48.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5dff31759eee997dbe1dae850fbdf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569ff6208a1c81a3bfba3f59fae3a8e5.png)
(1)当
时,求函数
的单调区间;
(2)当
时,方程
在区间
内有唯一实数解,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569ff6208a1c81a3bfba3f59fae3a8e5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f072c3a564e36a26d722e585379161ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0953444691256f713639f4ded91ff306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c34d2e40ee0263ecd6b6737c47bf98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfac1313a22cac7787e149e7663260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-02-08更新
|
1831次组卷
|
7卷引用:2017届天津市六校高三理上学期期中联考数学试卷
2017届天津市六校高三理上学期期中联考数学试卷广州市岭南中学2017届高三第一学期期中考试数学(文科)试题(已下线)2019年3月2日《每日一题》 选修2-2 【理科】周末培优河南省八市重点高中联盟2018-2019学年高二下学期领军考试理科数学试题陕西省宝鸡市千阳县中学2023届高三上学期一模理科数学试题陕西省宝鸡市千阳县中学2023届高三上学期一模文科数学试题(已下线)必考考点3 导数的应用(恒成立,不等式,零点) 专题讲解 (期末考试必考的10大核心考点)
名校
7 . 已知函数
,其中
.
(Ⅰ)若
在区间
上为增函数,求
的取值范围;
(Ⅱ)当
时,证明:
;
(Ⅲ)当
时,试判断方程
是否有实数解,并说明理由.
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573180520226816/1573180526641152/STEM/9f77109b36034e0bac29c16db8b02747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da989240786ef7c3e2d903f30caf59e3.png)
(Ⅰ)若
![](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/0a6936d370d6a238a608ca56f87198de.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ca761171c550f4a09d35e8eedb1c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a9041dd7f46ca1ce409c196c91a2bc.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ca761171c550f4a09d35e8eedb1c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629d20c6577097f4711cb269deaeeb87.png)
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2016-12-05更新
|
1044次组卷
|
2卷引用:2017届宁夏育才中学高三上第二次月考理数试卷
名校
8 . 已知函数
.
(1)求函数
的单调性与极值;
(2)若关于
的方程
有两个解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492ed70446f992ae9f02768fed444bbb.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d8757e551b2104d3dfbbd4c8bfe961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2016-12-04更新
|
598次组卷
|
2卷引用:2016届吉林四平一中高三五模文科数学试卷
2012·河北唐山·一模
9 . 设函数
.
(1)讨论
的单调性;
(2)( i)若
,证明:当
时,
; (ii)若方程
有3个不同的实数解,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2beb9de9d7aa2ee49bcc5fe32348456a.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)( i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb595535eaefe630a624adc02b713fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9351efff43e9446744faa1ea599dfc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342d52fc26cc550a45b80756903bee6.png)
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2012·河北衡水·一模
名校
10 . 已知函数
,其中
为常数,设
为自然对数的底数.
(1)当
时,求
的最大值;
(2)若
在区间
上的最大值为
,求
的值;
(3)当
时,试推断方程
是否有实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0473ffcca997f603b285fffbbfdfe39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8d82b0a97f17f6fbd0587cdfc984e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9378fdc21122404c708ea19feb2c9ea.png)
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