题目
题型:不详难度:来源:
![](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)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-15734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-72668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-60683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-76946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-36425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-89315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-86231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-48850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-71118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-58570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-92144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-64158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-39935.png)
解析
试题分析:(1)首先求出导数:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-35243.png)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043823-51453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-23806.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-54157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-35243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-22528.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-15734.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)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-69955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-69955.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-35243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-19921.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-49177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043830-64433.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/20191018/20191018043830-14983.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/20191018/20191018043825-91734.png)
试题解析:(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-35243.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-23806.png)
由二次函数奇偶性的定义,因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-54157.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-35243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-22528.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-15734.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)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043830-23858.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043830-19076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043830-60211.png)
只要
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043831-65312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-72668.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-35243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043829-19921.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-34215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043831-21280.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043831-88344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043831-35267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-45495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-80078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-13276.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-51230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-52747.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043833-63960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043833-28177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043833-79172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043833-53275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-14409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-28023.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-24393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-62979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-20168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043835-78552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-14409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043835-92915.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-58570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-92144.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043835-45412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043835-92359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043834-14409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043836-47073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043833-79172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043836-57940.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-92144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-52747.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043836-12280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-51230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043832-52747.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043836-86250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-58570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-92144.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-64158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-39935.png)
综上所述:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-60683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-76946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-36425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-89315.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043826-86231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-48850.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-71118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-58570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043827-92144.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-64158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043828-39935.png)
核心考点
举一反三
![](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)
![](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.![]() |
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