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解题方法
1 . 已知函数
.
(1)当
且
时,求函数值域;
(2)当
时,试讨论函数最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e43b36ff531cb8b20585f52d9cdbede.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a2cdf594729b651d9d8793939204c2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
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2 . 已知函数
.
(1)当
时,求该函数的最大值;
(2)是否存在实数
,使得该函数在闭区间
上的最大值为
?若存在,求出对应
的值;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b8933101840f2f4bc6bab038d7c167.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-02-19更新
|
602次组卷
|
2卷引用:内蒙古包头市2018-2019学年高一上学期期末数学试题
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3 . 已知函数
的最小值为
.
(1)当
时,求
;
(2)求
;
(3)若
,求
及此时
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce4c70e86489ca3fcb54fc3b28637e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb41f606e9e2cd3e826e0803ed1efed.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae95572621e2a14aff86e6cea5dddff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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4 . 已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778662c16848db470c6537705b8a839c.png)
若
的最小值为 - 3,求m的值;
当
时,若对任意
都有
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd737219d9b385af861192f4fc18e146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778662c16848db470c6537705b8a839c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239a01bf0f1b5d3926494316d23cf02f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310e1ebd3ac52132b7e33af907e28624.png)
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5 . 已知向量
, 设函数
.
(Ⅰ)求
的值域
(Ⅱ)设函数
的图像向左平移
个单位长度后得到函数
的图像,若不等式
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b63250166143c5eedc61f4232dc8f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4226122a52dd8b85dba2b840973fde.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅱ)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a92d3b12915c77dc770451249afaea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6 . 光波、电波、声波
,现实世界的波动现象无处不在,丰富多彩的波动现象大都可以用一族三角函数的叠加来刻画.已知某种波动现象对应的函数为
,其图象如下图所示.请你根据所学的数学知识,回答下列问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/ffe0a26f-4c6c-4be6-b1d1-bd167daf7e7a.png?resizew=411)
(1)求
的最小值,及取到最小值时
的取值集合;
(2)探究
在
是否存在零点,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f027e1e3dd39b5935c1ecd1dc4f04.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/ffe0a26f-4c6c-4be6-b1d1-bd167daf7e7a.png?resizew=411)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410189766b9081e21235d7a75eeef9d2.png)
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7 . 已知
,求函数
的最大值M(a)与最小值m(a).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f274f1247962a5b263183922fedfa086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73370fe2dd6dc4c5e13c59f1174974f.png)
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8 . 已知向量
,
,函数
,
.
(1)若
的最小值为11,求实数m的值;
(2)是否存在实数m,使函数
,
有四个不同的零点?若存在,求出m的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24029e5060944730e019af55f31c3d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23929564b68855be0bcddd09f88c8a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fe324cbbf388e74abb4d34fd2a433f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7197a0ef4462d9c49da2207a7588080.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在实数m,使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88039db503a206ca3e2f4f87f8cb0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320db668117654d39faa0c8ce830e9ea.png)
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2019-09-29更新
|
797次组卷
|
2卷引用:山东省济南市历城第二中学2018-2019学年高一下学期期中数学试题
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9 . 已知向量
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
(1)求
·
及
;
(2)若
,求
的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb34f494e53bbb24dddabb454e4827b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48062a415d81f451051af234dfa44774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07882aa0d4087bd4e551dbfa437e31d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27dbc69067bd921b66a06618584cb5ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2019-05-01更新
|
1224次组卷
|
5卷引用:【市级联考】山西省运城市2018-2019学年高一下学期期中调研测试数学试题
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10 . 设函数
=Asin
(A>0,
>0,
<
≤
)在
处取得最大值2,其图象与x轴的相邻两个交点的距离为
.
(1)求
的解析式;
(2)求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3206d37559fc605fec985aef86c629bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7824dcfd5ee3cf3aecf6773e717e7acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2df1bc516cf59796f7610454440afc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487e4c1900ac3f10118a1350137e7b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de12bbd5097debc83d6a46364589748.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8652dbb36294329e8c0c559cae88f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c75b327b3b9a41f71d462a83d5bf10.png)
您最近一年使用:0次
2019-03-05更新
|
1151次组卷
|
5卷引用:【全国百强校】北京市101中学2018-2019学年上学期高一年级期末考试数学试题