已知
,
.
(1)讨论
的单调性;
(2)若
有两个零点
,
,
是
的极值点,若
,使得
恒成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdac8719fed9bb4e1753587608265d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119f3d404a1fafb11b344b3bcf6af4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0d4a048ae3b16d560fe2e468e44a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
更新时间:2023-04-21 11:10:42
|
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解答题-问答题
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较难
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【推荐1】已知函数
(
是正常数).
(1)当
时,求
的单调区间与极值;
(2)若
,
,求
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74da4b06c434c46d5a8958ad77f2592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](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/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解答题-证明题
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较难
(0.4)
名校
【推荐2】已知
,其中
.
(1)当
时,分别求
和
时
的单调性;
(2)求证:当
时,
有唯一实数解
;
(3)若对任意的
,
都有
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae1d5e1ae68c2c1f7b46f65263c3c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab958eede2dbad749ba70bb230c88fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐1】已知函数
,其中
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(1)讨论函数
的单调区间;
(2)若函数
有两个零点
,
,且
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的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae4ce43e0df659276b6c7d40b730d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6657f5dd2a7723fcee6a7a10ca21d2d4.png)
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解答题-问答题
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较难
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【推荐2】已知函数
.
(1)讨论
的单调性;
(2)当
时,
,求
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f31c085a035b9e61e3b62c5c1ba9f3.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d07f9b89b24792b5e5cc639b399ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dfe106d15673f0dbfb5784db503c1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-问答题
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名校
【推荐3】已知函数
(
).
(1)当
时,求
的单调区间;
(2)若函数
有两个不同的零点
,
,证明:
.
(其中
是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8979242aa063e1f2a7b4e944a86b41b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae8d761c7aebbbc608bcdfb63a01ea4.png)
(其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
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【推荐1】已知函数
,且
在
处取得极值,
.
(1)证明:函数
存在唯一的极小值点
;
(2)若
,且当
时,
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f77abf65029bf4014dfea70aded594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9029bb3c2bb6b876c8973a343e8590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6330540758a21f46fc7a6d1e6328d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226126cce647e4c45b620bcc85e8cc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解答题-证明题
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较难
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【推荐2】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)
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