1 . 记
.求函数
的导数,讨论函数
的单调性和极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9da8a992a5c12256cf5f38fd3ceb69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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解题方法
2 . 设
,函数
.
(1)请讨论该函数的单调性;
(2)求该函数在闭区间
上的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c150cdf147f53a5c6f4e024c862ce5dd.png)
(1)请讨论该函数的单调性;
(2)求该函数在闭区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ce23fd1d866c3a711875b7c5a1c13c.png)
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3 . 已知函数
,其中
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当函数
有且仅有一个驻点时,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c69103038c41f2665f7179299730c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-05-14更新
|
221次组卷
|
2卷引用:上海市市北中学2022-2023学年高二下学期期中数学试题
4 . 已知函数
的定义域为R,其导函数
的图象如图所示,则对于任意
,下列结论正确的是___________ .(填序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/1/7ed9b67e-b87c-42ba-acd8-e181f8dec6e3.png?resizew=129)
①
恒成立;
②
;
③
;
④
;
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ebaef33ec95792488f08b953ede2f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/1/7ed9b67e-b87c-42ba-acd8-e181f8dec6e3.png?resizew=129)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c91674248e2283c297ada5d512a2e8.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f890aeca44e0639b4ac84640d253f15c.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57efa20c90b7962f9444e7666a12288.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60025fe6bbfd7645844c9e3e7a5871e6.png)
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解题方法
5 . 求函数
的导函数,并由此确定正切函数的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457eb5e0000350b102d387a80cf3476b.png)
您最近一年使用:0次
解题方法
6 . 已知函数
.
(1)若
,求函数
的极值,并指出是极大值还是极小值;
(2)若
,求函数
在
上的最大值和最小值;
(3)若
,求证:在区间
上,函数
的图象在函数
的图象的下方;由此启发,给出以下结论成立的一个判断依据,“在区间
(a为常数)上,可导函数
的图象在可导函数
的图象上方”(不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb72786dd0e97bea91c33701cf0b0f1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e734b17201fe992be7775714e9558.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03db4ea1dcb63b22cf4e917df5db581e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52284539e00aa8e9384575ca0ad3bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae702c7fac150ca5052d2eb88ee0dfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次