名校
解题方法
1 . 若二次函数
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49986e3fabfd3720179d706c4235634c.png)
(1)求
的解析式;
(2)若函数
,解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49986e3fabfd3720179d706c4235634c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0e68fa290e09324b667fabae0b86f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ced7663afedcd81edd9462a46ff98f.png)
您最近一年使用:0次
解题方法
2 . 已知
,其中
,
.
(1)求
在
上为减函数的充要条件;
(2)求
在
上的最大值;
(3)解关于x的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5d3a189277c96f4ecc56337ba1aae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df9daf719817f5b036d1f048b752c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
(3)解关于x的不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9515c395bbebc656bb05a871f9f04c91.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:不等式
有实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d38d63ff0b082869ca23778c7490b1e.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fa125e8d3ab03ca6d9c72566bc76d7.png)
您最近一年使用:0次
2023-09-07更新
|
301次组卷
|
2卷引用:河北省邯郸市2024届高三上学期第一次调研监测数学试题
解题方法
4 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3473c109ec4d71f833dad76eb5d145.png)
(1)若关于
的不等式
在
有实数解,求实数
的取值范围;
(2)设
,若关于
的方程
至少有一个解,求
的最小值.
(3)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3473c109ec4d71f833dad76eb5d145.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfcbc3ffca28dadd8241999c35cb49c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91e6d30e5e96f240b538c55aa1da9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed0a706f0f99690a25194a4586cea66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790b807c406d6f22dc559b1ec16f9356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688955342aa1c114d7fcc04618974410.png)
您最近一年使用:0次
名校
5 . 已知函数
.
(1)当
时:
①解关于
的不等式
;
②证明:
;
(2)若函数
恰有三个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca766a161f9438aef446b1beb7de3c4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
①解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d80a96345f600468f0efb316ccd586.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1048afd2ea59732a2119a2863ed77b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-01-11更新
|
1236次组卷
|
4卷引用:中学生标准学术能力诊断性测试2021-2022学年高三上学期1月月考数学试题
6 . 已知函数
.
(1)解关于
的不等式:
;
(2)当
时,过点
是否存在函数
图象的切线?若存在,有多少条?若不存在,说明理由;
(3)若
是使
恒成立的最小值,试比较
与
的大小(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158e629d5227dd15de9da05f5a6aa751.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a822a5d7d8e596e41466e6ba3f74a7.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5030685d4bfdaba51d78d4678f3e101c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a6b3b128b4bce79a63cea8869b12f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53f9f1ec37560c23829d6da6d3996a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff883ef65b7078d86da530bc80173610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321fb1302b7fc326afe47b49d2a4309f.png)
您最近一年使用:0次
2024高三上·全国·专题练习
7 . 已知函数
、
,
的图象在
处的切线与
轴平行.
(1)求
,
的关系式并求
的单调减区间;
(2)证明:对任意实数
,关于
的方程:
在
,
恒有实数解;
(3)结合(2)的结论,其实我们有拉格朗日中值定理:若函数
是在闭区间
,
上连续不断的函数,且在区间
内导数都存在,则在
内至少存在一点
,使得
.如我们所学过的指、对数函数,正、余弦函数等都符合拉格朗日中值定理条件.试用拉格朗日中值定理证明:
当
时,
(可不用证明函数的连续性和可导性).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805cc5abd1128e45df7cad0a9e2045db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddf844e3848b8bf52c0ec506fe749c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e464a3586f84fcdf7d221619f8018144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffe604dac7e511c06aa339460743ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636a8d9e362e768e825a98afdea2bd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94df95ba3ef31cd7a065d112c619e88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7957f902f96c3adb9d374d92ff87d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486cdd923c2b4c92928b10ab6266e792.png)
(3)结合(2)的结论,其实我们有拉格朗日中值定理:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f944dbcd1a2a1cc595573f63b244e9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4cfd131ea8772fea719318c865c907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2982ec308d84c83d538a58dae3ff1569.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5f5a7cf79c07caa572cfee93371a91.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
,
为参数且
.
(1)函数
的值域为
时,求参数m的取值范围;
(2)当
时,若方程
有两个不等实数解
,
,完成以下两个问题:
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1bbb13de97bdd4126bbd91baee9db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b156f0540d4628d2e61aefdfeba74bb.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e409bdb06c6e71f137eca131ecd596.png)
您最近一年使用:0次
名校
解题方法
9 . 已知:函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ad23c0ef2d67af4844df5175b41ff1.png)
(1)求
的单调区间和极值;
(2)证明:
;(参考数据:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0891a54fcf7ccbd9e6b8680944bc580d.png)
(3)若不等式
的解集中恰有三个整数解,求实数
的取值范围.(三问直接写出答案,不需要详细解答,参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ad23c0ef2d67af4844df5175b41ff1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd2cd53f618f890b0711f833ecff7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80d0cbe26bbac441eceb3e71a29010e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0891a54fcf7ccbd9e6b8680944bc580d.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f0eb2dcdd8c486c0f3e0856e2e02a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7722e21105bd9b5610506279805ba53c.png)
您最近一年使用:0次
10 . 已知曲线
在点
处的切线方程为
.
(1)求a,c的值;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7823aa2ac66c00ce0f260f3147eb6a.png)
(3)若关于x的方程
有两个实数解
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e34dc94a3d9dc4677f75e0aac8e98da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96f623802cd414e590247155ad0d62b.png)
(1)求a,c的值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7823aa2ac66c00ce0f260f3147eb6a.png)
(3)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c9639ad329a88d242c2d6f37d7c456.png)
您最近一年使用:0次
2023-04-03更新
|
299次组卷
|
2卷引用:湖北省咸宁市鄂南高级中学2022-2023学年高二下学期阶段性检测(9)数学试题