1 . 已知函数
.
(1)求
的单调区间;
(2)若函数
恰有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c301a174488703fea8e2322df0496fd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70315d1e6011057dcf0e4d089b0ab56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
2 . 已知
,函数
.
(1)若
是增函数,求
的取值范围;
(2)证明:当
,且
时,存在三条直线
是曲线
的切线,也是曲线
的切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea07afc90c5e15a1eaae1187e710b1c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d72d23a933bc89bd056868419b1afb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8801df26d9cb76bc289b64a3a26902e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01796ee3c345e41396a5cc0cf1d7326c.png)
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2023-05-26更新
|
257次组卷
|
2卷引用:山西省省际名校2023届高三押题联考(三)数学试题
3 . 已知函数
.
(1)讨论函数
在
上的单调性;
(2)若
有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b46c734f7c5ad829b17b0928c2e08.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85ede5c9b7d3a5ea7db6789670f17b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)求函数
的单调区间与极值.
(3)若对任意的
,都有
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1e9cdc69a5d80dbef0fb871b0c1c41.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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2021-09-14更新
|
532次组卷
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4卷引用:山西大学附属中学校2022届高三上学期期中数学(理)试题
5 . 已知函数
,
.
(1)求
的单调区间;
(2)若
在
处取得极值,直线
与
的图象有三个不同的交点,求
的取值范围.若
的极大值为1,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82039cb8f157cdb540eb033f36571fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 已知函数
.
(1)若
,求实数
的取值范围;
(2)设
的极大值为
,极小值为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ae9c590045b246110a80573c361ff3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8a0f86edc5e8136f988bbebb4c5334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
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2019-04-29更新
|
1100次组卷
|
5卷引用:【市级联考】山西省晋城市2019届高三第二次模拟考试数学(文)(B卷)试题
7 . 已知函数
.
(1)当
时,求函数
在点
处的切线方程;
(2)对于任意的
,
的图象恒在
图象的上方,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38244616ee45ce9eb9a0df9555aacc0a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661e3f38c635165582128b423b80adb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8d2eb7149c8c98cd8e035b3c64df11.png)
(2)对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d9c89d2cd1fb46b1e71ad10227c098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a042ec887b963ef8d69f5217703a938.png)
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8 . 设函数
.
(1)求函数
的极小值;
(2)若关于x的方程
在区间
上有唯一实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fc15e5758bea65f6fbd863cc0a1718.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b55afa924ee48ca16234374b18802a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ab265ae2099e7ab2f609fafbf3aef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2018-11-06更新
|
1387次组卷
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5卷引用:山西省运城市景胜中学2019-2020学年高二下学期期末模考数学(文)试题
名校
9 . 已知函数
,
.
(1)设
,求
的最小值;
(2)若曲线
与
仅有一个交点
,证明:曲线
与
在点
处有相同的切线,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdab6a9f42a3448cc3fba0051ce85a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3add4264073f994d46b92542bcbbf9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cdc9a462275dcb8de0cf880604ddd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74314814cdc6fb803abb4692458af131.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da84f77c42beb3e7b9d0fa516990bd6.png)
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2017-05-18更新
|
851次组卷
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3卷引用:山西省太原市第五中学校2019-2020学年高三上学期10月月考数学试题