1 . 已知函数
.
(1)当
时,求
在
上的零点个数;
(2)求证:当
时,
对
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04f0356f325d9f3cbc94e8426065304.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc25055c6c6ab7e4bfd929d28acb4a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23efa380a58dc9663ba06dc249ce721.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75035035d9d58e26781abfd4fc4d0d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744d8e4ec21306ba4b152cdc7319d8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9376011de97004ad1c9cf10f229e70ea.png)
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2 . 已知函数
,
.
(1)当
时,研究
在
上的单调性;
(2)①求证:
;
②当
,
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc8a91b4563eb174267f22d15f9699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce40b411e39d4d9fc91c9addb362c51.png)
(2)①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4123b4b9e76a410c64a08c0a8c134664.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f97c1ffed90421df446e1b692087f92.png)
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3 . 已知函数
,
.
(1)当
时,求证:
在
上单调递增;
(2)若函数
在
上只有一个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1377433265e8691182b668e403b91f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4892a8c06e4b7cf413804e63292004.png)
.
(1)若
,
,判断函数
的单调性;
(2)若
,且对
,不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4892a8c06e4b7cf413804e63292004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650295a835d46ef212bf2db4cdfeb3c8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/935b4035585dfe624ebdd0c758c6ea89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8883dc4f5a8aab2b01398f243d460c.png)
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5 . 已知函数
.
(1)求函数
的单调区间;
(2)若
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891c3b61504044e5f1f675c0eb3dc7ac.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41bc57877dc371372dc4145d2b56f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c960fc862fd36db83082f5c50cd604b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec30573e9ef491771f219d4b2c22f78.png)
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6 . 已知函数
,
,
.
(1)求函数
的单调区间;
(2)若对任意
,
的图象始终在
的上方,求实数
的最大整数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ed99a74e126a05cb520f19c094020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c4c0688af1b9c1bb748ebc72dc59de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a323e016a1d051b62e5d26076bee30e.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7 . 已知函数
(
).
(1)讨论
的单调性;
(2)设
,若函数
有两个不同的极值点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dca377668811d6b06bcacda9228c040.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bafb84cd3f290d9c5920db47ff1180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59b4ae053a3f1e3d3ac7afaa9aac77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac59ef367ebf2e36b984c2f6fd913e9.png)
您最近一年使用:0次
8 . 已知函数
在
时取得极值 .
(1)求
的解析式;
(2)若函数
有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb4a74bda3f96140869a085b1a2c2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75144f29f9f5a7816e9340ef958827f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-02-22更新
|
535次组卷
|
2卷引用:【名校面对面】2022-2023学年高三大联考(11月)文数试题
9 . 已知函数
.
(1)讨论
的单调性;
(2)若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1006ed6e51bce1900af199b16355b8b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a727a475a643cf412ced18378bac6d.png)
您最近一年使用:0次
2024-02-22更新
|
296次组卷
|
2卷引用:【押题金卷】2022年普通高等学校招生全国统一考试理科数学试卷(B卷)
解题方法
10 . 已知
是函数
的导函数.
(1)求函数
的单调区间;
(2)设
为函数
的两个零点且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3594c792b8d4075943cc51ee44ad42eb.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684bcf84f0a266515bfafde0da903050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次