名校
1 . 给出定义:设
是函数
的导函数,
是函数
的导函数,若方程
有实数解
,则称
为函数
的.“固点”.经研究发现所有的三次函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
都有“固点”,且该“固点”也是函数
的图象的对称中心.根据以上信息和相关知识回答下列问题:已知函数
.
(1)当
时,试求
的对称中心.
(2)讨论
的单调性;
(3)当
时,
有三个不相等的实数根
,当
取得最大值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2b5ee1eabb64358a3d9db2349b6fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bbba1031f0abb943f65142c5d11f8a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace97a0f7c91d9e1a636cd76f369660d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-04-11更新
|
615次组卷
|
4卷引用:贵州省贵阳市第一中学2022-2023学年高二年级教学质量检测四数学试题
2 . 已知函数
.
(1)若
是
的极值点,求
的单调区间;
(2)若关于
的方程
恰有一个解,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877c82e59465d74808019c81c89a6f3f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac080d199a7d2d3dbc389050c51a8a96.png)
您最近一年使用:0次
2022-09-29更新
|
532次组卷
|
8卷引用:贵州省2023届高三上学期联合考试数学(理)试题
解题方法
3 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb20b5898c5ac5ffa1a3138e7ed74e8.png)
(1)当
时,求函数
的单调区间;
(2)设
对任意
,总有
成立,求实数a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/2cb20b5898c5ac5ffa1a3138e7ed74e8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f072c3a564e36a26d722e585379161ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624fac9fb9981309c6a5e2d07686a120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2428921c82d2ace53ade031fa21fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e205bdf2d20697b8a84de10347c8e484.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330aac4d09c91db1b636cfb3d819ac67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a66ee29a06caf509e137278020fd86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次