题目
题型:解答题难度:一般来源:不详
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-56034.png)
解析
试题分析:根据条件中
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-64060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-39383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-39822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-69217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-39822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-69217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-33131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-14330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-25799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-14330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032311-14330.png)
依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-99013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-46991.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-85839.png)
∴ 由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-64060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-19235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-47353.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-23602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-91051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-83119.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-20345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-28797.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-49246.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032314-39506.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032314-22357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032314-56233.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032314-46364.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032314-35492.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-98265.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-89305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-60249.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-13748.png)
另解:本题也可用下面解法:
1. 用单调性定义证明单调性
∵对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-53792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-91146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-59783.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-30350.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-55207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-89166.png)
同理
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-55207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-60172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-24424.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-13748.png)
2. 二次函数最值讨论
解:依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-99013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-46991.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-85839.png)
∴由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-64060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-19235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-47353.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-23602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-91051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-83119.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-20345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-22297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-64502.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-40224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-21311.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-11493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-55207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-26064.png)
1°当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-30546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-48847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-55207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-39667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-21597.png)
2°当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-31966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-50013.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-40395.png)
3°当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032320-71212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032320-79519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-55207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-39667.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032320-52753.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032320-27446.png)
3. 二次方程根的分布
解:依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-99013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-46991.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-76557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-85839.png)
∴ 由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032310-64060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-19235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032312-47353.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-23602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-91051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-83119.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032313-20345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-22297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-64502.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032317-40224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-21311.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-11493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032316-55207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032318-26064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032320-25884.png)
1°当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-78245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-25711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-15189.png)
2°当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-38494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-29460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-58981.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032321-15189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032319-39667.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032322-29641.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-13748.png)
4.用均值不等式(下学段不等式内容)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032314-46364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032322-79243.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032322-79331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032322-74848.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-89305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032315-60249.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032320-27446.png)
核心考点
试题【已知奇函数 f (x) 在 (-¥,0)∪(0,+¥) 上有意义,且在 (0,+¥) 上是增函数,f (1) = 0,又函数 g(q) = sin 2q+ m 】;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/20190818/20190818032306-54134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032306-47207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032306-36923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032306-62703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032307-77941.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032258-82073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032256-93025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818032251-26472.png)
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