题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051644-42138.png)
(1)当x>0时,求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051644-97184.png)
(2)是否存在实数a使得在区间[1.2)上
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051644-61675.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051644-50240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-46155.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-10356.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-34619.png)
(3)由第一问得知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-26741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-75187.png)
解析
试题分析:解:(1)明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-52974.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-39043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-32123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051646-17524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-32123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051646-71586.png)
(2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051646-79610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051646-95764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051646-58121.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051647-57192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051647-40263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051647-34270.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051647-54332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051647-18786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051648-16934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051648-62471.png)
另
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051648-75166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051648-48654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051649-60902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051649-77279.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051649-87708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051649-44602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051649-54281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051650-29846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051650-41787.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051650-15956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-34619.png)
(3)由第一问得知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-26741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051645-75187.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051650-70086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051650-77942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051651-16313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051651-94706.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051651-94683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051651-81500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051652-47680.png)
点评:主要是考查了导数在研究函数单调性以及函数的最值和不等式的证明中的运用,属于难度题。
核心考点
试题【函数(1)当x>0时,求证:(2)是否存在实数a使得在区间[1.2)上恒成立?若存在,求出a的取值条件;(3)当时,求证:f(1)+f(2)+f(3)+…】;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/20191018/20191018051636-82177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051637-56880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051637-89644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051637-80254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051637-40617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051638-64495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051625-56916.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-19135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-77668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-59155.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-69248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-39158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-93071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-51812.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051626-41758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051627-71455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051627-65834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051627-28674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051607-94157.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051607-80606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051607-28424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051608-43961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051608-14516.png)
(2)关于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051608-93929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051608-94309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051608-14516.png)
(3)对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051609-91012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051608-93929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051609-20061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051609-15731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051609-36866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051610-21727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051609-91012.png)
“分界线”.设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051610-60614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051609-91012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051610-72399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-32502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-45681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-41396.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-32502.png)
(Ⅱ)在(Ⅰ)的条件下,求经过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-87035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-32502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-27084.png)
(Ⅲ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051556-55677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051557-85312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051548-80131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018051548-94334.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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