题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180307-33867.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-10444.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-10444.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-70963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-82043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-53764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-49137.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-10444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-89433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-12059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180308-10444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-67187.png)
(3)实数a的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-32669.png)
解析
试题分析:⑴ 先根据函数解析式求出
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-60689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-23778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-35086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-49719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-81185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-69470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-68688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-67187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-38792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-72187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-41899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-97657.png)
试题解析:⑴ 因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-85649.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-60689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-69470.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-37607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-68688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180313-55135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-12059.png)
⑵ 由⑴,
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180313-59864.png)
因为当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-35086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-49719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-81185.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-69470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180313-45237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-67187.png)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-68688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180309-67187.png)
⑶ 因为存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180313-60984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-38792.png)
而当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180313-26927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180314-31060.png)
所以只要
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-72187.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180314-31864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-49719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-68688.png)
![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() |
![]() | 减函数 | 极小值 | 增函数 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180311-68688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180315-36971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180315-76074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180313-26927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180315-77181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180316-26404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180315-77181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180316-78133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180316-44369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180316-49074.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180316-38823.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180317-58148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180317-74160.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180317-78543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180317-39334.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180317-43630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-97657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180318-47231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180318-68127.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-41899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180318-15817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180318-79130.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-97657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180319-65785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180319-91466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180319-16737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180319-20921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180319-51331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180312-41899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180320-51975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180320-71905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180320-68258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180320-73035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180320-93769.png)
综上可知,所求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180321-35339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180310-32669.png)
核心考点
试题【已知函数(1)求函数在点(0,f(0))处的切线方程;(2)求函数单调递增区间;(3)若∈[1,1],使得(e是自然对数的底数),求实数的取值范围.】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180253-38796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180253-15281.png)
(1)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180253-38952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-74222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-24427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-51824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-21733.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-63784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180253-38952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-74222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180255-13416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180255-13416.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180255-34835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-63784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180253-38952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-74222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180254-51824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180249-16034.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180249-32081.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180250-26526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180249-32081.png)
A.① | B.② | C.②③ | D.③④ |
A.(-∞,-1) | B.(-∞,2![]() |
C.(-1,2![]() | D.(-2![]() ![]() |
①当x>0时,f(x)=ex(1-x);②函数f(x)有两个零点;③f(x)>0的解集为(-1,0)∪(1,+∞);④∀x1,x2∈R,都有|f(x1)-f(x2)|<2.
其中正确命题的个数是( )
A.1 | B.2 |
C.3 | D.4 |
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