1 . 函数
的导函数
的图象如图所示,以下命题正确的是__________ .
是函数
的极值点; ②
是函数
的最小值点;
③
是函数
的极小值点; ④
在区间
上单调递增
⑤
在
处切线的斜率大于零; ⑥
是函数
的驻点也是极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddd46c180401ad4e86b9ef4d5883721.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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2 . 设函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e8f84dbff14410f60ee3ac26089de1.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e8f84dbff14410f60ee3ac26089de1.png)
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名校
3 . 抛物线
的焦点坐标是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a56449ad6dd65aec7525c94273f59.png)
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4 . 已知二次曲线
的方程为:
,当m,n为正整数,且
时存在两条曲线
,其交点P与点
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f219575dd7bb6c3d8912a0d6d81a294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e00a9e5172c28e6895801dc9c53134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d51de84ea16fc5553ba3d588f379f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce67f2138e7295cd72d66b2908cb6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
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解题方法
5 . 若
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076e3d56a889b208a3d66788f9643ccd.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2bb30b7cc00ad0327d6e495407a4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076e3d56a889b208a3d66788f9643ccd.png)
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6 . 若函数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389f233195d7a44b87503bbc08ecdd6e.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3652d61b9a0a46978bf1836a40b7d222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389f233195d7a44b87503bbc08ecdd6e.png)
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7 . 双曲线具有如下光学性质:从一个焦点发出的光线经双曲线反射后,反射光线的反向延长线一定经过另一个焦点.已知双曲线
,如图从
的一个焦点
射出的光线,经过
两点反射后,分别经过点
和
.若
,则
的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0839d0d1164c1ffc0de32d32c7da3321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3015eea1309a7cea34438008d082233d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3255ac740cb137a24777208940455dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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8 . 设
,
是椭圆
与双曲线
(
,
)的公共焦点,曲线
,
在第一象限内交于点M,
,若椭圆的离心率
,则双曲线的离心率
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ab2caccd742eb636bd8378661a8807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f1ea30341eb5d584710c3aebc64ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec3537c9300e8b7a5c1eed6fb0b6e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
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9 . 已知
是曲线
上的动点,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a96e1302cb4c8462387cf6e2ba60706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c20a186564dd89dd59415428beb5747.png)
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10 . 已知双曲线
的右顶点为
,点
都在
上,且关于
轴对称,若直线
的斜率之积为
,则
的渐近线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40c376377e4a31da4dc4a007e976de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
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