题目
题型:解答题难度:简单来源:不详
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044704-14372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044704-62700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044705-20696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044705-99124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044705-85932.png)
(1)求常数a,b,c的值;
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044705-95830.png)
(3)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044705-12092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-28793.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-22945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-22372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-33898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-55442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-53297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-22110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-72933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-27117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-39511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-76413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-39511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-79130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-91340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-72544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-94876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-97885.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-10926.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-78491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-23293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044710-53560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044710-14964.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-23293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044710-17429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044711-20724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044711-72103.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044711-21801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-23293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044711-73425.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044711-21801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-23293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044711-82799.png)
由①②③,得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-22945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-22372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-33898.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-20926.png)
因此,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-59358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78630.png)
要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-23019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-23019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-91576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-23019.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-35392.png)
(ⅰ)当函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-23019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-12049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-47018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-78689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044714-24160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044714-19952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-47018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044714-95806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044714-53671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044714-86366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044715-74936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044715-45011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044715-58910.png)
(ⅱ)当函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-23019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-12049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044713-47018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044712-78151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044715-69813.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044715-42896.png)
综上,实数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-59836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044706-55442.png)
(3)由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-48304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-56190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-13396.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-53268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-63620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044717-24121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-53297.png)
由函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044717-24121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044716-56190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-53297.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-22110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-72933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044717-25371.png)
亦即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044707-27117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-39511.png)
亦即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-76413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-39511.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-79130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-91340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044708-72544.png)
…
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-94876.png)
所以有
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044717-75422.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044709-10926.png)
点评:本题第一问题型基础简单,第二问需要分情况讨论,对学生有一定的难度,第三问需要借助于单调性求出最值进而转化为恒成立的不等式,难度大
核心考点
试题【.(本小题满分12分)已知函数,是常数)在x=e处的切线方程为,既是函数的零点,又是它的极值点.(1)求常数a,b,c的值;(2)若函数在区间(1,3)内不是单】;主要考察你对函数的单调性与最值等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044702-99464.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044656-36164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044656-91437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044656-91437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044656-42218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044656-42218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044651-23915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044651-47727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044652-97860.png)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044640-11682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044640-62294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044640-67605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044640-47149.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044640-94649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044641-70644.png)
(2)若各项为正的数列
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044641-99453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044641-11839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044641-20518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044641-29822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044642-29409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044642-64182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044641-11839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044642-12175.png)
(3)在(2)的条件下,证明:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044642-40892.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044632-39601.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044632-56978.png)
(2)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044632-74076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044633-51821.png)
(3)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044633-75161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044633-14997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818044633-99609.png)
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