1 . 已知函数
,记M(a,b)是|f(x)|在区间[-1,1]上的最大值.当a、b满足M(a,b)≤2时,
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa1d3a1cf44dd03bcf70678b2999e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd73344268aa345e9be954264a45c87.png)
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2 . 已知
,试求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a31c4a4cedc3088d78a01ed4928a981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
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2019-01-28更新
|
591次组卷
|
2卷引用:2018年全国高中数学联赛河南省预赛
3 . 已知
、
、
均为正数,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f15e1577e547599fe74de17e637f41.png)
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2007高一·河南·竞赛
4 . 定义在
上的奇函数
满足
,且当
,
,时,有
.
(1)证明:
是
上的增函数;
(2)证明:当
时,
;
(3)若
对所有的
,
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821632252680978d2619aacec310e64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bc2eeaca8a8ce4bcce2bff011a11bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b84952d33957e5b90d8cd3b3bcc127.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08829c3ec099f3427ede9062d19a78c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51035f9b1a84d36570e1eefa1386a6a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb2922de7222b364f096db55a57e926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
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2007高一·河南·竞赛
5 . 函数
的最小值为.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3270a88e731668e90332491977505621.png)
A.90 | B.171 | C.190 | D.45 |
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2011高二·河南·竞赛
6 . 函数
的最大值为 __________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d89ad604e5dc7a5c80dc2d13f4f65df.png)
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10-11高一下·江苏连云港·期末
7 . 已知锐角
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f49b5d4807884f3dae8a47719ce4d02.png)
,若
,(1)求
的表达式;
(2)当
时,求(1)中函数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1c8146d084248c9c65dd8a11801905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f49b5d4807884f3dae8a47719ce4d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493585dbefe67b1b876f0d391b19a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90984954a048f7b4559b90a8618ac149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa7af8f87b4f540eefe5aa180677ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
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8 . 设
,且
恒成立.则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd0f1e3e3b41948f1b3d287c4b0cb44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d9dd9cf07f855ed94680cb6601a6e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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9 . 若
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476809afe0708f5b896af5b1d7acbb8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1838291076ff96070c4b60e106cb29b.png)
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10 . 若不等式
的解集为
,则二次函数
在区间
上的最大值、最小值分别为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d466f06147310b34624ce018cf58d6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe2283d104437709bc336d139789251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fd40daa0af9627c9defbfb5a2c2837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2018-12-15更新
|
191次组卷
|
3卷引用:2005年河南省数学竞赛_高一试题