名校
1 . 已知函数
,其中
.
(1)若
单调递增,求b的取值范围;
(2)若
,函数
有三个极值点
.
(ⅰ)求b的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9a97b7adbb319f0e1e4c53cc677b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ae717593e6c3197f3da28730579c1e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca9db228d7fea1fda455eb514251736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1617bb5dc942c9d9e5c0516630179b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcee20976de0e0e8c1ccd7a951674691.png)
(ⅰ)求b的取值范围;
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0622eedb58c740432a093b3680dcc4aa.png)
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2 . 已知函数
.
(1)若
在定义域内单调递减,求
的取值范围;
(2)若
在点
处的切线斜率是
, 证明:
有两个极值点
,
,且3
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cc1567cb0d64861cf4141cf7ff4168.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81455ecba5fd243339019655422b021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6536ea889cb510d0c97fb83f836276d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef2864f0f2f7911502deda088a06a6c.png)
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名校
3 . 已知函数
.
(1)若
在
上不单调,求a的取值范围;
(2)当
时,记
的两个零点是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
①求a的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c565eed01da8f81dcb33909bd65d16f1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dcdd87d593df4a5c5e98d47fe1cfa6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
①求a的取值范围;
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b6f58e3f5d77e2acad79e7656688c6.png)
您最近一年使用:0次
2020-07-04更新
|
751次组卷
|
2卷引用:浙江省宁波市宁海中学2020-2021学年高三(创新班)上学期高考模拟数学试题
2022·浙江·模拟预测
名校
解题方法
4 . 已知
,
,
,
,
.
(1)求
的单调区间;
(2)若
在区间
上单调递增,求实数a的取值范围;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b195180c8b0c44ad2e6b636b36ec7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a5dfb075eef48c4a3066b98df27fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5700e556aa93919d75b23b8a0f739a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd34bc2979bfed0fa99269635dde578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9ae83fb55592dba217f18fdb8dde97.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4b3829d3c35b92f86f6019b5a73d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f325f9278565b29cb271a68cf14c6e.png)
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