解题方法
1 . 已知函数
.
(1)若
是函数
的极大值点,函数
的极小值为
.
①求实数
的取值范围及
的表达式;
②记
为
的最大值,求证:
(
是自然对数的底).
(2)若
在区间
上有两个极值点
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caa4139ae3ce1f7c9271bd072a71c17.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2ac429737efebf150a1bd088ba846.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2ac429737efebf150a1bd088ba846.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ef957460e2108cd4d257fc140597c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561cb11261a996c0960d626fd18f4e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0825fbec45b977025a3df012ec5963.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e78a499596d8d268faf03f37e86cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446dcad9c82048efb3ab2ca034695b97.png)
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名校
解题方法
2 . 已知直线
分别与函数
和
的图象交于点
、
,现给出下述结论:①
;②
;③
;④
,则其中正确的结论个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/501a6d50c937729c8d0f02b2b62a0ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2eff609c6043c2a89a6dd163fe2244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](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/419504736c4934f6e0df4114c3743944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f700e9e84ec901bf75313a29757740fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c6510c0a13618cb9cad14172480c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f76409bffa66c2157ea8bac43cede7.png)
A.4 | B.3 | C.2 | D.1 |
您最近一年使用:0次
2021-10-28更新
|
1763次组卷
|
7卷引用:江西省师大附中2020届高三三模考试理科数学试题
江西省师大附中2020届高三三模考试理科数学试题(已下线)对点练15 对数与对数函数-2020-2021年新高考高中数学一轮复习对点练河南省信阳市罗山县2021-2022学年高三上学期第一次调研考试数学(文)试题(已下线)5.3 导数在研究函数中的应用(难点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)第5章 导数及其应用 单元综合检测(难点)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)辽宁省大连育明中学2022-2023学年高三上学期期中考试数学试题吉林省长春北师大附属学校2021-2022学年高三上学期期中考试数学(理)试题
3 . 已知函数
,过
作切线交函数图像于点M和点N,记
,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5e228803048cbc40f6aa7141d3a80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7f445c1f0fee62251250433d8d6288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0b73676954dd9e4f79d2426f2f5260.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2021-08-30更新
|
252次组卷
|
2卷引用:2017年清华大学429学术能力测试数学试题
4 . 设正整数
使得关于
的方程
在区间
内恰有
个实根
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64170fd8ac03379ffe24249e730000d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40622f9501f8a4e6eb8a3bb13bb655f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acd5e05f89802149b8b810c24d6ac73.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() ![]() ![]() |
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5 . 设直线
,曲线
.若直线
与曲线
同时满足下列两个条件:①直线
与曲线
相切且至少有两个切点;②对任意
都有
.则称直线
为曲线
的“上夹线”.
(1)已知函数
.求证:
为曲线
的“上夹线”;
(2)观察下图:
的“上夹线”的方程,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70087bf78bee970f6ecf583ca1fccc42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0016d106579d6b26cf2960cf744f317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9dc155203792c9983b2118b7730088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c043c3bf7b638f8bb635ee098130560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)观察下图:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08fe48eafb7a58cb673cc4bce2aa0e7.png)
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6 . 已知
为自然对数的底数,
.
(1)求
的单调区间;
(2)证明
有且仅有两个零点;
(3)问:函数
与
的图象有几条公切线?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6bf7c3198cdd4dafc81e3992f34bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f184f195e983df4014e6c57a2e7ee67.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575df2758d348d7d5b889fb5ad8ddafe.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575df2758d348d7d5b889fb5ad8ddafe.png)
(3)问:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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