已知函数
.
(1)讨论
的单调区间;
(2)若
存在极大值M和极小值N,且
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4734f79e736cf70657beff494ead95.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6ab5dc88d360f758ee6709bd2a787f.png)
更新时间:2022-03-17 21:22:07
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解题方法
【推荐1】函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/824567f7737a62ac120b0dadc44e6263.png)
(1)讨论
在区间
上极值点个数;
(2)若对于
,总有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d197fc404f8ee2495aea94c8569ded50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/824567f7737a62ac120b0dadc44e6263.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(2)若对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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适中
(0.65)
【推荐2】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4950df1e229c9436fd9106d2b22eb92d.png)
(Ⅰ)若
是
的极小值点,求实数
的取值范围及函数
的极值;
(Ⅱ)当
时,求函数
在区间
上的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4950df1e229c9436fd9106d2b22eb92d.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.png)
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【推荐3】已知函数
.
(1)求函数
的图象在
处的切线方程;
(2)求函数
的极值;
(3)若
,且
对任意
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef71e2ccbb9921d239b96d23a5a386a6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99074f989e74d5ff306b4b7b7a379c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37388fb5ecd6aa6a89245f715c64ef2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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【推荐1】设函数
.
(1)若该函数为奇函数,求曲线
在点
处的切线方程;
(2)讨论函数
的单调性;
(3)若函数
有三个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8a3c215a4314bc7e995169dc23f5a4.png)
(1)若该函数为奇函数,求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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(0.65)
【推荐3】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664442ad85cb9bc16ff331c2697270f.png)
(1)当
时,求
的极值;
(2)讨论
的单调性;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e664442ad85cb9bc16ff331c2697270f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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