名校
1 . (1)在用“五点法”作出函数
的大致图象的过程中,第一步需要将五个关键点列表,请完成下表:
(2)设实数
且
,求证:
;(可以使用公式:
)
(3)证明:等式
对任意实数
恒成立的充要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467a953b54798b6e2dcd6d76f8817938.png)
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1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d95727eed094e7ceb6663ee9d39bda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141ba74bc522b95958aea59cdc8c93d0.png)
(3)证明:等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83576aaf57c7ebdcf56110fdbb0c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d8ae1706a9ea5df3eca17eaa5c8b71.png)
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解题方法
2 . 已知
,记
,
,
.
(1)试将
、
、
中的一个函数表示为另外两个函数复合而成的复合函数;
(2)借助(1)的结果,求函数
的导函数和最小值;
(3)记
,a是实常数,函数
的导函数是
.已知函数
有三个不相同的零点
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468e12e54a9f92597209394a014926e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d5ede4162743db1282c4c745d5b7c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117bafde8f721dfd6971cf4e9d2afcbd.png)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(2)借助(1)的结果,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e00ca9ac35e13b1aa6d614c7a74b471.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07af08f8917a80ef7609df0a89bd6d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e1fedba462890feb92a798b00314a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e03e21bbdc7f3ae80c1e504863c5294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24c1b603f987e08cd12944bab0181f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6c5505a43b336cb503e50975b5341a.png)
您最近一年使用:0次