上aa雨轩
春芽
共回答了12个问题采纳率:91.7% 举报
(1)
![](https://img.yulucn.com/upload/7/ac/7acfec32dbdf06efe0802d6089c2c3cb_thumb.jpg)
;(2)
![](https://img.yulucn.com/upload/3/76/376448e6e5b4e8f60461dc9860c6669b_thumb.jpg)
.
试题分析:(1)根据二次函数的最值建立方程组,即可求函数
![](https://img.yulucn.com/upload/b/10/b1008b3c62272b94fc0956906207a9c6_thumb.jpg)
的解析式;(2)将
![](https://img.yulucn.com/upload/e/39/e39034d6f05a394c7e294b875510cf4f_thumb.jpg)
在
![](https://img.yulucn.com/upload/8/54/854902329aa77fc1ffe5437df70959e8_thumb.jpg)
时恒成立进行转化为求函数最值,即可求出
![](https://img.yulucn.com/upload/e/63/e639a430dcbce10ca4e77debb3b63a7f_thumb.jpg)
的取值范围.求最值时考虑利用换元当将函数转化为求二次函数在一个闭区间上的最值.
试题解析:(1)∵
![](https://img.yulucn.com/upload/a/56/a567ecba7dedfcd19379e3a76b3e4b2b_thumb.jpg)
,
∴函数
![](https://img.yulucn.com/upload/b/10/b1008b3c62272b94fc0956906207a9c6_thumb.jpg)
的图象的对称轴方程为
![](https://img.yulucn.com/upload/c/d3/cd363e6a594b4eef3fd757619b04e868_thumb.jpg)
.
![](https://img.yulucn.com/upload/f/24/f246e6242218c7b45554edbc74404312_thumb.jpg)
依题意得
![](https://img.yulucn.com/upload/c/2c/c2c6f96363fabae72f8d48e87308fd18_thumb.jpg)
,即
![](https://img.yulucn.com/upload/9/e6/9e6ed5cf19e1950b26126bb12cbc23f8_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/1/97/1974dd30ecd8d7818a658bd56c05823d_thumb.jpg)
,
∴
![](https://img.yulucn.com/upload/7/ac/7acfec32dbdf06efe0802d6089c2c3cb_thumb.jpg)
.
(2)∵
![](https://img.yulucn.com/upload/2/e2/2e21addb20bc6510f4e00a7d6bab91aa_thumb.jpg)
,∴
![](https://img.yulucn.com/upload/c/8c/c8c7eb4cbcd644a032966ed5ab560307_thumb.jpg)
.
∵
![](https://img.yulucn.com/upload/2/61/2614eed1bb777844c033d02b8f8377ea_thumb.jpg)
在
![](https://img.yulucn.com/upload/8/54/854902329aa77fc1ffe5437df70959e8_thumb.jpg)
时恒成立,即
![](https://img.yulucn.com/upload/b/8c/b8c54d991e55cf44b3de90b40c5d84d3_thumb.jpg)
在
![](https://img.yulucn.com/upload/8/54/854902329aa77fc1ffe5437df70959e8_thumb.jpg)
时恒成立,
∴
![](https://img.yulucn.com/upload/9/ec/9ec6612f335b3341f31de73f7314b48e_thumb.jpg)
在
![](https://img.yulucn.com/upload/8/54/854902329aa77fc1ffe5437df70959e8_thumb.jpg)
时恒成立,
只需
![](https://img.yulucn.com/upload/2/98/2981ec73f322e6eee73a6915efaa01d9_thumb.jpg)
.
令
![](https://img.yulucn.com/upload/0/06/00648efdca82cc758b0ca7d637f9e177_thumb.jpg)
,由
![](https://img.yulucn.com/upload/8/54/854902329aa77fc1ffe5437df70959e8_thumb.jpg)
得
设
![](https://img.yulucn.com/upload/8/3a/83af4fd1f5dfd294b89393853129afe7_thumb.jpg)
,
∵
![](https://img.yulucn.com/upload/0/c6/0c6b7fd30ee26bfc1e4784d15a994362_thumb.jpg)
,
∴函数
![](https://img.yulucn.com/upload/d/cf/dcf95afaf8cfd7a2a360e1c7c8dd150f_thumb.jpg)
的图象的对称轴方程为
![](https://img.yulucn.com/upload/b/d5/bd505372c7223f0e4e9261aaf37e502f_thumb.jpg)
.
当
![](https://img.yulucn.com/upload/5/42/542c6d599471df9da3f7773023b1c577_thumb.jpg)
时,取得最大值
![](https://img.yulucn.com/upload/c/cb/ccb438d4e98f7cb3accdf1a7a6c67602_thumb.jpg)
.
∴
![](https://img.yulucn.com/upload/2/55/2550b6206c197e2b008b867f10123898_thumb.jpg)
∴
![](https://img.yulucn.com/upload/e/63/e639a430dcbce10ca4e77debb3b63a7f_thumb.jpg)
的取值范围为
![](https://img.yulucn.com/upload/3/76/376448e6e5b4e8f60461dc9860c6669b_thumb.jpg)
.
1年前
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