名校
解题方法
1 . 建造一个容积为
、深为
的无盖长方体形的水池,已知池底和池壁的造价分别为120元/
和80元/
.
(1)求总造价
(单位:元)关于底边一边长
(单位:
)的函数解析式,并指出函数的定义域;
(2)求总造价
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edc5717c841dd4af6209a340c943785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
(1)求总造价
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
(2)求总造价
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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名校
2 . 已知
恒成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b0a83c2cae2575227d395aa023134d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
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3 . 已知
均为正实数.
(1)当
,求
的最小值;
(2)当
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0914de472ead84fb45ee3dda781f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b8d3564d7ae5687f69b64b150c4b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
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4 . 设
均为正数,且
,则
的最小值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a026c07ed4818c25a70c2abb60f8de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf99adccc80f28343fedd8d0aad7429.png)
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解题方法
5 . 下列函数中,值域为
的是
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa311daf7a73f8c45de4462f9d92b6.png)
![](https://img.xkw.com/dksih/QBM/2023/11/13/3367128233566208/3367148311642112/STEM/05b42ca71bc149538c2db18fdcb97243.png?resizew=4)
A.![]() ![]() | B.![]() |
C.![]() ![]() | D.![]() |
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名校
解题方法
6 . 已知
,且
,
(1)求
的最小值;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9338b4562fe2d41548310e5208837bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce460941cf3ff54ccb6aec5085689a91.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4e9d49707bfa309667af1aa57f1281.png)
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7 . (1)已知
,求
的最小值及取最小值时
的值;
(2)已知
,
,
,求
的最大值及最最大值时
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b398e30b66e74b63086e9b3531090c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2436951e9a6f5ca0fc0ae65b9d787119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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名校
解题方法
8 . 在
中,a,b,c分别为内角A,B,C所对的边,
.
(1)求A;
(2)若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1948773eeedd3b8aecc17a56579b145a.png)
(1)求A;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57770796a401eef8d7144a98a42ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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9 . 已知
为正实数,且
.
(1)求
的最大值;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195d55fe82646a1deeafb3a68676b2db.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f29d5f376c75c41ae6af0c8a8565449.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fc838e1477179b36ca7481ee2cc1e8.png)
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解题方法
10 . 不等式
对
恒成立,则
的取值范围____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc98cbb53d44b6b56ec175527c6ea47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90918b116ddc7dd7115ece5520dbd006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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