名校
1 . 给定函数
.
(1)求函数
的单调区间,并求出
的极值点;
(2)若关于
的方程
有两个不同的解,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdfe48038034eb671b3852e261c24f3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 给出定义:设
是函数
的导函数,
是函数
的导函数,若方程
有实数解
,则称
为函数
的.“固点”.经研究发现所有的三次函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
都有“固点”,且该“固点”也是函数
的图象的对称中心.根据以上信息和相关知识回答下列问题:已知函数
.
(1)当
时,试求
的对称中心.
(2)讨论
的单调性;
(3)当
时,
有三个不相等的实数根
,当
取得最大值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbb68078590e8785def6cb1d7e0126a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2b5ee1eabb64358a3d9db2349b6fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bbba1031f0abb943f65142c5d11f8a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace97a0f7c91d9e1a636cd76f369660d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-04-11更新
|
616次组卷
|
4卷引用:重难点突破04 三次函数的图象和性质 (七大题型)
3 . 给出定义:设
是函数
的导函数,
是函数
的导函数,若方程
有实数解
,则称(
)为函数
的“拐点”.经研究发现所有的三次函数.
都有“拐点”,且该“拐点”也是函数
的图像的对称中心,已知函数
(1)求出
的对称中心;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c553558c1640e17b0c67395627d488c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f087ded8039eedaa8aa724b81ec393e9.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88afe5c5be8dc12217ccbef588cc61c.png)
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解题方法
4 . 设函数
.
(1)若
,求证
有极值,求方程
的解;
(2)设
的极值点为
,若对任意正整数
都有
,其中
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85aa2e4d5f2fe4f49d72e2302a1585d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed085cc685f0bf1b3df2ed16e04ccea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b00438433719b82971f9fe309e04b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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5 . 已知函数
,
.
(1)
,
,求
的最小值;
(2)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4ee544faff9e49a41d9b69827501b.png)
①证明:
;
②若方程
有两个不同的实数解
,
证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d23c80f11dcb3f7537c88cbd76a1267.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f042768ad824aad2aed73a44193856c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4ee544faff9e49a41d9b69827501b.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3799b7e05fda170b8f661643a1685bbc.png)
②若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32051bf94998f88eecff75846cc750b0.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/901a1ca166c6ddf5ae7a7cb7d66431b0.png)
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名校
6 . 在英语中,实数是Real Quantity,一般取Real的前两个字母“Re”表示一个复数的实部;虚数是Imaginary Quantity,一般取Imaginary的前两个字母“Im”表示一个复数的虚部.如:
,
;
,
.已知复数z是方程
的解.
(1)若
,且
(a,
,i是虚数单位),求
;
(2)若
,复数
,
,且
,
,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2feba771ef35780fd3730a7f64e92af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f180e675d09eb3f38d45b5178fda797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03f55ee5dd80c3d6c4993bf2b4bfe9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be07a99ddc4d937071dd7b68a25f6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0d4d254ff83c9298b1eecb3b4c831c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6aecd620e40fe87a8ad3230bc91deaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4111b5bb1c41cc93d75f29a9539afd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d165b3397aab477869842a16b7ff6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff0f1b6dd0be54207299f6c22eec25f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b896385877f1431f7cb6039c6d4e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee3a3acbc491caa282b95be84300be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476d332663b8fc357c1a3fc85f9fa5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f07c0d81d401253c3a9d48c9428a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d3e597e6175d602094521e85d58e99.png)
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2023-04-14更新
|
261次组卷
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3卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期第一阶段学业质量联合调研抽测(4月)数学试题
7 . 已知关于
的方程
,
.
(1)当
时,在复数范围内求方程的解;
(2)已知复数
,若方程
有虚根,求
的模的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5aedc701158c3368168565085cb6569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f7f23e7f20dd8bc65a4967cd306782.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc05f2cb5cf6f0356039cce674b01d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5aedc701158c3368168565085cb6569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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2023-04-12更新
|
527次组卷
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2卷引用:河南省信阳高级中学2023-2024学年高一下学期5月期中测试数学试题(二)
名校
解题方法
8 . 已知函数
.
(1)求
在
的最小值;
(2)若方程
有两个不同的解
,且
成等差数列,试探究
值的符号.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33426d6f89e2874a389b5d884fa5a4de.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce90064385c4633056784c1ae375a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546cd7c7c03fde940c6f3d4b3d423061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
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2022-11-17更新
|
926次组卷
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6卷引用:河北省武邑中学2023-2024学年高三上学期1月期末考试数学试题
名校
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4e6107be46de0bb91fcecb65b9ee2a.png)
(1)若1是
的极值点,求a的值;
(2)求
的单调区间:
(3) 已知
有两个解
,
(i)直接写出a的取值范围;(无需过程)
(ii)λ为正实数,若对于符合题意的任意
,当
时都有
,求λ的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4e6107be46de0bb91fcecb65b9ee2a.png)
(1)若1是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3) 已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df628874faa615d0cf49e38c6b9968a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(i)直接写出a的取值范围;(无需过程)
(ii)λ为正实数,若对于符合题意的任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7ea8007570536864a5cf4b00a8d2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafb39935a3b8eee7b2529063ab3fda6.png)
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2022-10-30更新
|
1621次组卷
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7卷引用:微专题09 隐零点问题
10 . 对于三次函数
,定义:设
是函数
的导函数
的导数,若
有实数解
,则称点
为函数
的“拐点”.现已知
.请解答下列问题:
(1)求函数
的“拐点”A的坐标;
(2)求证:
的图像关于“拐点”A对称,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47db775f5675cd10012f964a336832f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4a5292f6af433342a866336d05fe5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de68bc1a57041a038aea6711c8848999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4724249ffd113d05e9a1806c90647e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44497598c08c9e219a7737af9faa1d87.png)
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2022-09-30更新
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6卷引用:第01讲 导数的概念与运算-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)
(已下线)第01讲 导数的概念与运算-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(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)河南省南阳市第一中学校2022-2023学年高三上学期第二次阶段考试文科数学试题山西省晋中市平遥县第二中学校2023届高三上学期10月月考数学试题(已下线)1.2.2 函数的和差积商求导法则(同步练习)2022-2023学年高二选择性必修第二册素养提升检测(提高篇)(已下线)5.2 导数的运算(2)