设函数
,若存在
,使得
成立,则实数a的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf75f2d1a146dd3d5a3cf1779b84e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49353a2ad04d5efed79d7849e4ea493.png)
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2023·全国·三模 查看更多[3]
天一大联考皖豫名校联盟2023届高三第三次考试数学试题(已下线)模块九 第1套 1单选 2多选 2填空 2解答题(解析几何 导数)辽宁省铁岭市昌图县第一高级中学2022-2023学年高二下学期期中数学试题
更新时间:2023-04-22 09:09:48
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【推荐1】形如
的函数称为“幂指型函数”,它的求导过程可概括成:取对数——两边对
求导——代入还原;例如:
,取对数
,对
求导
,代入还原
;给出下列命题:
①当
时,函数
的导函数是
;②当
时,函数
在
上单增,在
上单减;③当
时,方程
有根;④当
时,若方程
有两根,则
;
其中正确的命题是___________ .
![](https://img.xkw.com/dksih/QBM/2015/8/13/1572213723824128/1572213729624064/STEM/9c83f4d6d11a43228d4c05ce5e4d12df.png?resizew=96)
![](https://img.xkw.com/dksih/QBM/2015/8/13/1572213723824128/1572213729624064/STEM/044baa459b384f96bbad0149f2aaeb72.png?resizew=15)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc032cda1dedf229d7df873c2e9ca27.png)
![](https://img.xkw.com/dksih/QBM/2015/8/13/1572213723824128/1572213729624064/STEM/044baa459b384f96bbad0149f2aaeb72.png?resizew=15)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0077ce48cda2bfe03ffe631582e15f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817d35bf12761370754183a7e0fcf544.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0733e8dfacbad67bdb7c26930acddaf.png)
![](https://img.xkw.com/dksih/QBM/2015/8/13/1572213723824128/1572213729624064/STEM/9c83f4d6d11a43228d4c05ce5e4d12df.png?resizew=96)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7739562253090217642fe8bf5a0e68bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075a7c95e87c5be50b369870d7e5a789.png)
![](https://img.xkw.com/dksih/QBM/2015/8/13/1572213723824128/1572213729624064/STEM/9c83f4d6d11a43228d4c05ce5e4d12df.png?resizew=96)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13202c77e96a1182b5c9d1928732a732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaf016a015aa7f69be7c343069617df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5b0e81bc12b5bd60cbd3dbe1c51ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb070ee9705d6d38a3639353a5bfcd69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b743bdec6a7d1eacc2550c59bd7e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5a5442c98d30d1b552bb43b68221f2.png)
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其中正确的命题是
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【推荐2】定义在
上的函数
满足
,
的导函数,且
对
恒成立,则
的取值范围是_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d21a983f17e7a2685413e95c7b63c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156d42bdd57f0a8a33887156553d0380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
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【推荐3】已知定义域为
的偶函数
,其导函数为
,满足
,则
的解集为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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解题方法
【推荐1】已知正实数
,满足
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9304cd1934dfd1b3749a161e8cfa7f3.png)
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解题方法
【推荐2】定义在R上的函数
,若
的解集为[1,+∞),则a的取值范围为____________ .若关于x的不等式
恒成立,则a的最大值为_____________ .
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【推荐3】已知函数
与
的图像上存在关于
轴对称的点,则实数
的取值范围为_________
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