名校
解题方法
1 . 已知函数
,
为
的导函数.
(1)证明:当
时,函数
在区间
内存在唯一的极值点
,且
;
(2)若
在
上单调递减,求实数
的取值范围.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81894c7f92af1cac020a4172c8911287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fefd1d1687c2274b0544028573413d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fac8237d2038f0758be704b2ef4087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d126b5824164e145c4764ad0b79396a8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3cee5e50ee4f1dfbcf0ff0312fef1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44db6e470168bf9ebed4494ccc593e5.png)
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