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
,则称点
为函数
拐点.已知
.
(1)求证:函数
的拐点
在直线
上;
(2)
时,讨论
的极值点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a53de2e60c85b2044ed87efc5b76b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a53de2e60c85b2044ed87efc5b76b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.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/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b6db145f3e561e3d16b8e58b62550a.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dfc9e95cade14ae9b7fc89519a2dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1447dbe580ac5c825776995118e75acf.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91029148ad78d9cd3e7c26704b3c77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
2020·湖南邵阳·三模 查看更多[2]
更新时间:2020-08-07 07:58:17
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解答题-问答题
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【推荐1】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25ab4f80679d9ee97529f7bd3dd4c29.png)
(1)若
,证明:
存在唯一极值点.
(2)若
,证明:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25ab4f80679d9ee97529f7bd3dd4c29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d30e582553a6e95f13fd7ddb571f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddc641f2dfa5191b020bb82253934f9.png)
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名校
【推荐2】已知函数
,在点
处的切线为
.
(1)求函数
的单调区间;
(2)若
,
是函数
的两个极值点,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bd6d144442c008fa3d42448844b15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff5ccd7a2aeb75b46df3742f05ef71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ae417b17a6133b185088c768265dc1.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4d14516ce86b6120e03d119ce2f304.png)
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【推荐3】已知函数
.
(1)讨论函数
的单调性.
(2)若
,设
是函数
的两个极值点,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c908fd0aeed73b99925ba8fc824c7b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aee3e5cf1f3f193f8b279b8cdd3ba2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
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解题方法
【推荐1】已知函数
,如果存在常数
,对任意满足
的实数
,其中
,都有不等式
恒成立,则称函数
是“绝对差有界函数”
(1)函数
是“绝对差有界函数”,求常数
的取值范围;
(2)对于函数
,存在常数
,对任意的
,有
恒成立,求证:函数
为“绝对差有界函数”
(3)判断函数
是不是“绝对差有界函数”?说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c413f613d1bb2dfbfc9969f82416196a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876a24bd55b56b1b1222895018eeb33c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dec717182be7265a9a11f65068da359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a1e7412ce026da3be8b80117426f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3021f33d4044c903de28d926911a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c413f613d1bb2dfbfc9969f82416196a.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329731df2bbd762126f4e7df01cb188c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062f2074ff3e5e5e72e20f4d066f0e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f20b947d584a1dc48676c2ae6e2af52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ecdccf4a334ea959a456533c40d53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062f2074ff3e5e5e72e20f4d066f0e9d.png)
(3)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c266b102e4db9bcbb5a1e4ca16c9253a.png)
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【推荐2】若函数
的图像上有两个不同点
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(1)试判断函数
与
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(2)若
,求函数
的图像的“自公切线”方程;
(3)设
,求证:函数
的图像不存在“自公切线”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b09e2d46f94b9ca3caf3f8283619c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e7e79ac17c51c7a4aaf9d59ec9beb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ff968467d6dd3c1ec36ffbd43a3d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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