1 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678bfff2980a71f3b3e48c998fb2acce.png)
A.![]() ![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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名校
2 . 已知函数
,
,
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edf7b602025a4f0585ad7f0e5d5db5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5672d1944e82d69d81edcdd8223bdeb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
A.![]() ![]() | B.![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() ![]() |
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解题方法
3 . 已知
,
,且
在点
处的切线与直线
垂直.
(1)求实数
的值.
(2)若
的图象经过原点,且
,当
时,
过点
的切线至少有
条,求实数
的取值范围.
(3)若
,且
,其中
,
均为正实数.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2dc19a078760863c7e681e59e0ec56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8bb7e252de0e54ca82ad2c36ffba37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227d4946b9dbfdc8bef33b42b6a82572.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbab1a525c4451a43041defaa18a98f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9fab43d7bc79776880a47091152b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa70fa7eb86c3733e2c1f1c7d07dd802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7892b90ae2ff71fd827c95e5aabc3049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca96bf407a3ba46ef3c59c5eee4137c.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/803b13fac1480b428cb4ee4555852024.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)证明
存在唯一的极值点
(3)若存在a,使得
对任意
成立,求实数b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2611ed88afaf272aa770d1c56541c87e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若存在a,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32d3d61a2d4ab562f3e83ff307ded69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
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2023高三·全国·专题练习
5 . 已知函数
的图象在点
处的切线方程为
.
(1)用
表示出
;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b198677e91defa3ffba5e1865eb387c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb168665b95f30538130eb97fc99f722.png)
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6 . 已知点
是抛物线
:
的焦点,直线
:
与
相交于
,
两点,过点
,
分别作
的切线交于点
,点
是弦
的中点,点
是线段
的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0189d4c890b2f150fc4ab7664a86294c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.![]() | B.直线![]() ![]() |
C.点![]() ![]() | D.![]() |
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2023-12-30更新
|
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3卷引用:云南省昆明市云南民族大学附属高级中学2024届高三上学期12月月考数学试题
名校
7 . 已知曲线
:
(
).
(1)讨论函数
的单调性;
(2)设曲线
与曲线
关于y轴对称,过曲线
上任意一点
作直线
,
与曲线
分别相切于
,
两点,试求出直线
与曲线
所有公共点的坐标 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61e21039b34316d2e3ac6f38b7da529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0480cedb2d254f3820e7e35ee33fb459.png)
(2)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3fe038d038e0af2185ddbb89a11629d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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解题方法
8 . 已知函数
图象上有一最低点
,将此函数的图象向左平移
个单位长度得
的图象,若函数
的图象在
处的切线与
的图象恰好有三个公共点,则
的值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8bc5f394b15d6c20c6f8c5e13ba2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba71568baea8c394a6a1d339f4985078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c90d414358eed73f510f830337d758.png)
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2023-12-28更新
|
847次组卷
|
4卷引用:江苏省南通市海安高级中学2024届高三上学期12月月考数学试题
江苏省南通市海安高级中学2024届高三上学期12月月考数学试题山东省泰安市新泰中学2024届高三上学期期末仿真模拟数学试题广东省广州市铁一中学2024届高三上学期一模数学试题(已下线)考点7 函数y=Asin(ωx+φ)的图象、性质 --2024届高考数学考点总动员【练】
9 . 设函数
,
.
(1)若函数
在点
处的切线方程为
,求a,b;
(2)若方程
有两个不同的实数根,求b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/382110585cc4e1bfd63f868983e3adef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cba078e3e36effe1825c41c572a494.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e7417618db2a984a0b1637b03e4174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a354a07a24b8ad2e137db8c244730ae9.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8bfb563f79688d136e0cb958b5153c.png)
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|
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3卷引用:山西省吕梁市孝义市部分学校2024届高三上学期12月月考数学试题
山西省吕梁市孝义市部分学校2024届高三上学期12月月考数学试题山西省晋中市灵石县第一中学校2024届高三上学期12月月考数学试题(已下线)2023-2024学年高二下学期第一次月考解答题压轴题十六大题型专练(1)
名校
解题方法
10 . 函数
在
处的切线方程为
.
(1)求
;
(2)已知
,过
可作
的三条切线,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377172ac328ddfc4ff2613c772941bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4e112fa3f0203666503fb979fab562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c194728f50d927d7f6b16682a7c25f.png)
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