题目
题型:不详难度:来源:
![](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)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-79912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-52668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-25374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-43530.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-62652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-41719.png)
解析
试题分析:(1)首先求出导数:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-49008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-91935.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-91638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-79791.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-79912.png)
(2)首先求出函数的极大值点.又由题设:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-51251.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-71813.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-95238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-17238.png)
注意它的两个零点的差恰好为1,且必有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-55652.png)
结合导函数的图象,可知导函数的符号,从而得到函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
试题解析:(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-91935.png)
由二次函数奇偶性的定义,因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-91638.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043809-79791.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-79912.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-71813.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-95238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-17238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-55652.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-69806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043811-58454.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | + | 0 | - | 0 | + |
![]() | 递增 | 极大值 | 递减 | 极小值 | 递增 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043812-93009.png)
又由题设知:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-52668.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-22531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-71813.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-95238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043810-17238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043812-12984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043812-63466.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-25374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043813-84447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043813-51993.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-43530.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043813-39400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043813-19998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043814-71568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043814-20243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043814-89910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043814-24236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-41719.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043814-35618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043815-33441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043814-89910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043815-76889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043815-67337.png)
综上所述, 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-25374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-43530.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-62652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043808-41719.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-81213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-16277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-38751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-64206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-12258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-58927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-81213.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-45422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-45223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-91389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043800-92786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043800-76720.png)
A.2 | B.3 | C.4 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-30012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-73944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-33343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-52592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043746-68781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043746-93321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043747-64025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043747-98449.png)
A.![]() | B.-![]() | C.![]() | D.-![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043740-90384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043740-76210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043740-67630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043740-88824.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043735-76993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043735-97680.png)
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