名校
解题方法
1 . 有一圆柱形的无盖杯子,他的内表面积是
.
(1)试用解析式将杯子的容积
表示成底面半径
的函数;
(2)定理:若
,则
,当且仅当
时等号成立.
阅读下列解题过程:求函数
的最大值.
解:
,当且仅当
,即
时等号成立,所以
时,
的最大值为
.
问:当杯子的底面半径为多少时,杯子的容积最大,最大容积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12d5b15f6979cd665d54fd17341fc2f.png)
(1)试用解析式将杯子的容积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b785a4b6636ed1f145ed8f7e3a0fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be6e964c405a9cdf6623f9219898fd3.png)
(2)定理:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0c9fd7b50fc20cc3e7c0bd4442c306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162cd9270205b4e891f7e806abe01bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
阅读下列解题过程:求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896cf6a3fcde580b4cd78431ba255d0f.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68661d53ba9a388797dc9a42595a593d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25359e135f750694a9103837dbc9a291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280878aa2e6d5580178cc6c99229b9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280878aa2e6d5580178cc6c99229b9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738bc12c4d44438814ce6f606fda695a.png)
问:当杯子的底面半径为多少时,杯子的容积最大,最大容积是多少?
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