1 . 设
,满足
.
(1)证明:若
,则当
时,
.
(2)若存在
满足
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e761714f6940c2c06c5750e2ed80cc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbd27b6b4143c730ab9d36393a5fe14.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c61cfbfd3bf888856b7dc9b2a84c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac247d375e0da7fddafad1aa8186aa51.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4439c7de7291f79def06d548603de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
您最近一年使用:0次
2 . 对三次函数
,如果其存在三个实根
,则有
.称为三次方程根与系数关系.
(1)对三次函数
,设
,存在
,满足
.证明:存在
,使得
;
(2)称
是
上的广义正弦函数当且仅当
存在极值点
,使得
.在平面直角坐标系
中,
是第一象限上一点,设
.已知
在
上有两根
.
(i)证明:
在
上存在两个极值点的充要条件是
;
(ii)求点
组成的点集,满足
是
上的广义正弦函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3037bb4ec2e6dfb182b22df30899cab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2dfbd59c0d4efc09e09ad82e83e431.png)
(1)对三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2c831570d29c0fcbe5da38473ee828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d6fa911e3396b34fb470c10b063fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7121bf913ba5f136cb6d35db030ed70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c287a0f6a3521b83db37422a1aa309bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944ede342597c070831052dc06bca45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe4d0e11cd9b9421c4d18121ffd181a.png)
(2)称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7041eb865c44a89770acd4fd71024bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9919ff015350c4e25aa0c05c09c329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56f913087e3bbf8cd9dd7c9bba7dc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c65d3d6119b18fd2427497cbd413c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2232cbe8d56d936da2ea9c3a78d87f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce43981e5251e382690797f24907de2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d97b51756740950b8a9304755b4224.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42027a6a90b0a513981ebd5ed4431460.png)
(ii)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa6d6bca6428b15c6e95504904e944.png)
您最近一年使用:0次
名校
3 . 已知函数
,
.
(1)若
,
,求
的单调区间;
(2)若函数
是函数
的图像的切线,求
的最小值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972efbd8ad14fb73877c222172b18e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e542fc34c94ba82d6646cac06257050.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f442c662903757d09fb284c4fc2eec10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2316563595e29fd4279845ab8afc5ba2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e542fc34c94ba82d6646cac06257050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972efbd8ad14fb73877c222172b18e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee599f1b7f0bbbbe786d00b7c27eccca.png)
您最近一年使用:0次
2017-03-20更新
|
1318次组卷
|
3卷引用:第十四届高二试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)