题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043916-43083.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043917-62817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043917-64735.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043917-10595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043917-46069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043917-67792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043918-31096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043918-30666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043918-14102.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043918-22777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043918-89656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043919-78176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043919-94065.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043919-48615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043919-99861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043920-15939.png)
解析
试题分析:(1)利用导数分析函数的单调性,然后由单调性确定函数的最值;(2)先由导函数求出点P处的切线斜率,然后由恒成立条件,转化为求k的最大值,从而求出实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043920-45364.png)
试题解析:(1)依题意,知f(x)的定义域为(0,+∞),
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043920-38407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043920-36886.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043920-31517.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043921-78023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043921-20885.png)
当x>1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043921-44596.png)
所以f(x)的极大值为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043921-12036.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043921-74937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043922-12968.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043922-63615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043922-97728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043922-88878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043919-99861.png)
(3)因为方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043923-61579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043923-97010.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043923-31961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043923-24396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043923-61746.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043924-32557.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043924-60466.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043924-29538.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043924-53653.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043925-81133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043925-33641.png)
因为m>0,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043925-66431.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043925-70789.png)
因为h(1)=0,所以方程(*)的解为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043925-11817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043926-60496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043920-15939.png)
核心考点
试题【设函数 (1)当时,求函数的最大值;(2)令()其图象上任意一点处切线的斜率≤ 恒成立,求实数的取值范围;(3)当,,方程有唯一实数解,求正数的值.】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043906-87220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043906-96304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043907-75519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043907-39561.png)
(1)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043907-87654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043907-51477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043907-16761.png)
(ⅰ)求证g(x)为单调递增函数;
(ⅱ)求证对任意x
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043908-91683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043908-30576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043908-60561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043908-47438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043908-91683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043909-55554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043908-30576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043909-21226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-61875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-66383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-66383.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-91655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
(Ⅱ)若在区间(0,e]上至少存在一点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-15435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-95552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-66383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-99252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-11770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-34163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-50318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-19474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043842-78951.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043823-55228.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043823-51453.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-12204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-38132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-69955.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-34215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-91437.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-49008.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-29575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-80843.png)
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