名校
1 . 已知函数
.
(1)讨论函数
的单调性;
(2)若关于
的方程
有两个不相等的实数根
,
(i)求实数
的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b60a9d7e2cffc60990a65d9b645ca8.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795224255225a95de529b1de8aca1a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb3f4a42fbe4c7c522a707a24b17076.png)
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141d819347adf2c2c8f2bd2c99115809.png)
(1)求函数
的极值;
(2)当
时,求证:函数
有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141d819347adf2c2c8f2bd2c99115809.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8f867196410e2828e2bbd3183b02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b141970f41e90ca87ef417ca440202a1.png)
,
(1)当
时,函数
的最大值是_____________ ;
(2)若函数
无最大值,写出一个满足条件的
的取值是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b141970f41e90ca87ef417ca440202a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
4 . 已知函数
在区间
上不单调,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5742c2575dc451f89c03326f44edd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 函数
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da6e156a3038c0c00e364fc6176d90a.png)
A.0 | B.![]() | C.1 | D.![]() |
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6 . 已知函数
.
(1)若
,求函数
的极小值;
(2)讨论函数
的单调性;
(3)若
,令
,且
在
上不单调,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8f1d8a058b06f6e92bfef08a6e1cc4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e7e2521bc77d291d6bcbd1195c865c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990ffebc9fb1838660453460645ed21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ce82779a834a6871c96515eaaa5571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 已知函数
,过坐标原点
作一条直线
与曲线
相切于点
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff85da28e039c245b56bb390e83dd829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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8 . 一球沿某一斜面自由滚下,测得滚下的垂直距离
(单位:
)与时间
(单位:
)之间的函数关系为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd22909035604651c8946242a5d3930.png)
A.前![]() ![]() | B.在时间![]() ![]() |
C.前![]() ![]() | D.第![]() ![]() |
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9 . 已知函数
,则曲线
在点
处的切线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0af89a62c43d2b1d44886a6d4fadbf64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 已知函数
,则( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbca215afda7ce7fbd22fd0928a11a8.png)
A.函数![]() ![]() ![]() | B.函数![]() ![]() |
C.函数![]() | D.函数![]() ![]() |
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