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1 . 已知函数
(
)在其定义域内有两个不同的极值点.
(I)求a的取值范围;
(II)记两个极值点分别为
,且
.已知
,若不等式
恒成立,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5124251b521fb2525f55b99ee9ff6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(I)求a的取值范围;
(II)记两个极值点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5def2e680848aaf69b5a8c0f50ce05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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10卷引用:四川省成都市石室中学2022届高三上学期期末数学(理)试题
2 . 已知函数
,曲线
在点
处的切线与
轴交点的横坐标为
.
(1)求
;
(2)证明:当
时,曲线
与直线
只有一个交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85417b79b6eae94c7eefd460272c42bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2817c52144d06555e98131b5e657c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8041c797b98b834c70dbf7d1d4346.png)
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10卷引用:四川省雅安市2016-2017学年高二下学期期末考试数学(理)试题
四川省雅安市2016-2017学年高二下学期期末考试数学(理)试题黑龙江省牡丹江市爱民区第三高级中学2018-2019学年高二下学期期末数学(文)试题天津市红桥区2018-2019学年高三上学期期末文科数学试题贵州省三穗县民族高级中学2021-2022学年高二上学期期末考试数学(文)试题2014年全国普通高等学校招生统一考试文科数学(全国Ⅱ卷)黑龙江省哈尔滨市第六中学2018届高三10月阶段考试数学(文)试题(已下线)专题09 导数的综合应用-十年(2011-2020)高考真题数学分项(已下线)专题04 函数导数及其应用-十年(2012-2021)高考数学真题分项汇编(全国通用)(已下线)专题04 导数解答题-2(已下线)专题22 导数解答题(文科)-2
2014·江西上饶·二模
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3 . 已知函数
.
(1)当
时,求函数
在
上的最大值;
(2)令
,若
在区间
上为单调递增函数,求
的取值范围;
(3)当
时,函数
的图象与
轴交于两点
,且
,又
是
的导函数.若正常数
满足条件
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8069113f5f6c47e4d72f2a3890af7d7e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7fefece0cf6660a409832f72dff95.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b9ff3088cf75d2c0723095b849155a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed18bd80c6c4142f68e89f4ad44570b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caaa5229151d3101a125c2cb82d7424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4a57fa701747e4b70ce26eb18ab8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4516485edd9fa7a96ce7c3694624ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e1c19b1ccb1ababd42f72e9fead0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ea91586599a572adb9e7c3e86b5415.png)
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