2011·四川·一模
1 . 已知函数
的导函数为
,且不等式
的解集为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ef47a9c5e90d1182a799ea2497a8af.png)
(1)若函数
的极大值为0,求实数
的值;
(2)当
满足不等式
时,关于
的方程
有唯一实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890b333c8fe8206b6c023122abfc049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62559d143b4a977be9990eebcbec539e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ef47a9c5e90d1182a799ea2497a8af.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80a7ce5328f6abc0b9112c3f18cd3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28a8dc742d5612da5ec999c10c30fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2014·江苏徐州·三模
2 . 已知函数
.若存在实数
,
,使得
的解集恰为
,则
的取值范围是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcfd03c005a1d38ee09ec4ddeab0671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2011·浙江金华·三模
3 . 已知函数
,
.
(1)若F(x)在x=1处取得极小值﹣2,求函数F(x)的单调区间;
(2)令f(x)=
,若f′(x)>0的解集为A,且满足A∪(0,1)=(0,+∞),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25c0df3fb46ea5937d4cb24ef33cb1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffab54b733feb2f8a7fb468b783f374.png)
(1)若F(x)在x=1处取得极小值﹣2,求函数F(x)的单调区间;
(2)令f(x)=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0bbe4d31d570b5875ca1713620ece1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95358717841874f91bca7f938da6592.png)
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4 . 已知二次函数f(x)=x2+x的定义域为D恰是不等式
的解集,其值域为A,函数g(x)=x3﹣3tx+
的定义域为[0,1],值域为B.
(1)求函数f(x)定义域为D和值域A;
(2)是否存在负实数t,使得A⊆B成立?若存在,求负实数t的取值范围;若不存在,请说明理由;
(3)若函数g(x)=x3﹣3tx+
在定义域[0,1]上单调递减,求实数t的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572464821477376/1572464827678720/STEM/16633df644954b0d9ad870d69b770af6.png?resizew=52)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572464821477376/1572464827678720/STEM/b66521a14d5342b8a93533b39b224e3b.png?resizew=20)
(1)求函数f(x)定义域为D和值域A;
(2)是否存在负实数t,使得A⊆B成立?若存在,求负实数t的取值范围;若不存在,请说明理由;
(3)若函数g(x)=x3﹣3tx+
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572464821477376/1572464827678720/STEM/b66521a14d5342b8a93533b39b224e3b.png?resizew=20)
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