2024高三·全国·专题练习
解题方法
1 . 已知函数
.
(1)若函数
有三个零点分别为
,
,
,且
,
,求函数
的单调区间;
(2)若
,
,证明:函数
在区间
内一定有极值点;
(3)在(2)的条件下,若函数
的两个极值点之间的距离不小于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077315c5a7b12294497294e536831d77.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f5cd91996571c9da95e6f26bc80661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23292eca257af6a97309ee40ce6cbf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37f19a2ad8f24cf63bff68be15faa67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799f6009a476fa056e1af71f26dd2fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(3)在(2)的条件下,若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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2 . 我们熟悉的网络新词,有“yyds”、“内卷”、“躺平”等,定义方程
的实数根
叫做函数
的“躺平点”.若函数
,
,
的“躺平点”分别为
,
,
,则
,
,
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be943c6bb7e170907c93eae6b13a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d997e3fd54416a529c5095523bc15e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17c20662a07a25d11f33a4488e31cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13487a3c7d84a5638de224a370910012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
3 . 若函数
存在零点
,函数
存在零点
,使得
,则称
与
互为亲密函数.
(1)判断函数
与
是否为亲密函数,并说明理由;
(2)若函数
与
互为亲密函数,求
的取值范围.
附:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6cf17ce69359ec8ccf933ad8357a53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db18e638db2fb367cfe10bfaee37229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e60075f5d53066c03f106346dada26.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca6aff55f526b90cf606b04c9985c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c25df9ceeca0a576686820cb294ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c292239a48d1475428eeb9863d5dceb.png)
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解题方法
4 . 函数
的零点所在区间是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699b3f84d2e5beea2370a910cd0c6599.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 若函数
在
上是单调函数,且满足对任意
,都有
,则函数
的零点所在的区间为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d30155644641e0bd5f22e8cd37dee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知函数
,数列
满足
,函数
的极值点为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b049efe281685d1d9b7a5ccad33bbb.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248a4fa4b5ca53a58f6e05073698c98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f568095732e8c853cf406b7d317b5ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ddeda8fdd7bc1b0c7ff6f456f5451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b049efe281685d1d9b7a5ccad33bbb.png)
您最近一年使用:0次
7 . 若函数
存在零点
,函数
存在零点
,使得
,则称
与
互为亲密函数.
(1)判断函数
与
是否为亲密函数,并说明理由;
(2)若
与
互为亲密函数,求
的取值范围.
附:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35b13df9d8831bb4368e7036488675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db18e638db2fb367cfe10bfaee37229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e60075f5d53066c03f106346dada26.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe2f63cdc7606986d6250facf20ad1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfd7245d512a98d9105f843c094c7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c292239a48d1475428eeb9863d5dceb.png)
您最近一年使用:0次
2024-06-16更新
|
214次组卷
|
4卷引用:江西省部分学校2023-2024学年高二下学期第二次月考(5月联考)数学试题
名校
8 . 将函数
的图象向右平移
个单位长度,得到函数
的图象,则函数
的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4201223cfcf158b600f5c72407e32b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2660bdb91f09c1a2a719bb54539f59f1.png)
A.1 | B.2 | C.3 | D.4 |
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|
114次组卷
|
2卷引用:湖南省娄底市第三中学2023-2024学年高二下学期5月月考数学试题
名校
解题方法
9 . 已知
为方程
的根,
为方程
的根,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb0bd07a0eec6d37efe8f2e310b5420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06143cdf12d19aa34f0a1e60feeb787.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-06-13更新
|
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3卷引用:福建省泉州市安溪第一中学2023-2024学年高二下学期5月份质量检测数学试题
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dee348f72cf9f9f0c7abac4f49b0c11.png)
(1)讨论函数
的零点个数;
(2)若函数
在区间
上取得最小值4,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dee348f72cf9f9f0c7abac4f49b0c11.png)
(1)讨论函数
![](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/7754cc9374c8193dadb6875fb8a3fefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次