1 . 定义
是
的导函数
的导函数,若方程
有实数解
,则称点
,
为函数
的“拐点”.可以证明,任意三次函数
都有“拐点”和对称中心,且“拐点”就是其对称中心,请你根据这一结论判断下列命题:
①存在有两个及两个以上对称中心的三次函数;
②函数
的对称中心也是函数
的一个对称中心;
③存在三次函数
,方程
有实数解
,且点
为函数
的对称中心;
④若函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac322fc4206da717226ad89530effdd5.png)
.
其中正确命题的序号为_______ (把所有正确命题的序号都填上).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b589732202941f828016f982c92996b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60a6d986c80039124c8a869b0e481af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
①存在有两个及两个以上对称中心的三次函数;
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c087948f0abff7f6b3218860c973f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc139f70df469a51f530e03c98abaa.png)
③存在三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a42dfca9f27abe558892fc0b7db96df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb0c68f6e69ab9da3ea2c8c2f48f683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed0aa12ed308e80e35f1bb6101d36d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b8df99b8a0839cba0eb04427c0a1b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac322fc4206da717226ad89530effdd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb688d1f5aa60c67b53486b84f0aa432.png)
其中正确命题的序号为
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2 . 已知函数
有两个极值点,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d31c72ff02d72eccbb8d05118a2566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414b758a27b2f3d3e814777b5a64028c.png)
(1)当
时,求函数
在
处的切线斜率及函数
的单减区间;
(2)若对于任意
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414b758a27b2f3d3e814777b5a64028c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e777e5ab19259943eb6b541426d5416a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e2d2273f9bb50a7081c8c79854d3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知函数
.
(1)求
的单调区间;
(2)若对所有
都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3b6c56aee4bb8a8131fd960415c745.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对所有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95fb7dcca58c4d43f29ffdc8ba5f2583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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13-14高三·山东淄博·阶段练习
名校
5 .
,其中m>0.
(1)当m=1时,求曲线y=f(x)在点(1,f(1))处的切线的斜率;
(2)求函数f(x)的单调区间与极值;
(3)已知函数f(x)有三个互不相同的零点0,x1,x2,且x1<x2,若对任意的x∈[x1,x2],f(x)>f(1)恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c885512e04912921ac2550a66439fea6.png)
(1)当m=1时,求曲线y=f(x)在点(1,f(1))处的切线的斜率;
(2)求函数f(x)的单调区间与极值;
(3)已知函数f(x)有三个互不相同的零点0,x1,x2,且x1<x2,若对任意的x∈[x1,x2],f(x)>f(1)恒成立,求m的取值范围.
您最近一年使用:0次
2016-12-04更新
|
449次组卷
|
5卷引用:河南省信阳高级中学2022-2023学年高三上学期开学考试数学(文)试题
河南省信阳高级中学2022-2023学年高三上学期开学考试数学(文)试题(已下线)2015届山东省淄博实验中学高三第一次诊断性考试文科数学试卷2016届江苏省盐城市盐阜中学高三上12月月测数学试卷天津市芦台一中2019届高三年级第四次模拟考试数学(文)试题江苏省徐州市2022-2023学年高三上学期期中复习数学试题
6 . 已知函数
,若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0efe2cd30db16fe0bae0daae4e7e649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43bac11d412479a24f00e4c20f92b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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2016-12-03更新
|
181次组卷
|
3卷引用:2015-2016学年吉林省长春市十一中高一上学期期初考试理科数学试卷
7 . 已知函数
的定义域为
,若对于任意的
,都有
,且当
时,有
.
(Ⅰ)证明:
为奇函数;
(Ⅱ)判断
在
上的单调性,并证明;
(Ⅲ)设
,若
(
且
)对![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1152fe51a6add4d6263e52829cd3c6b.png)
恒成立,求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/18633b78c3d9438b94abb4a45eff94d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef2201f734c80e9279d0e76101e0f75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca823539e05fcd713b956d72b963c6d7.png)
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/fb82211d4e79434ba3885a20b2066ee2.png)
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/1e376c0ea10e4f1e97d746a569f9a949.png)
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/c8bd636b76d64988acd740687444dee6.png)
(Ⅰ)证明:
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/18633b78c3d9438b94abb4a45eff94d3.png)
(Ⅱ)判断
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/18633b78c3d9438b94abb4a45eff94d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef2201f734c80e9279d0e76101e0f75.png)
(Ⅲ)设
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/5f77f4609b72427b9b4f034be56e7ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed53293efd1d9326b02824a653207486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d281e837adac1f8bf88a944e106aa305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1152fe51a6add4d6263e52829cd3c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e7183391ed1f553dd8e0c8d684e457.png)
![](https://img.xkw.com/dksih/QBM/2015/10/28/1572274430844928/1572274436939776/STEM/a22a136a126d4d1783df4e63c446016e.png)
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8 . 已知函数
.
(1)当
时,求函数
的单调区间;
(2)
时,令
,求
在
的最大值和最小值;
(3)当
时,函数
图像上的点都在不等式组
所表示的区域内,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73318bc7cb2d5fc9a2a5c6b9f864873c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2806feb02d7c96484db00771ae757a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b3bc04b7060d5b3d289736e2c4faaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811c6fbc93bafee69ded75316ef05122.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955a2d0ee5cc78a9da2c8559712d1bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020f4a69b7124a7ddbebf63f1b3fa0d4.png)
您最近一年使用:0次
2016-12-03更新
|
469次组卷
|
2卷引用:2016届山东省潍坊中学高三上学期开学考试理科数学试卷
解题方法
9 . 如图所示,一根水平放置的长方体枕木的安全负荷与它的厚度d的平方和宽度a的乘积成正比,同时与它的长度
的平方成反比.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/5/edf9e7aa-06e6-4f60-9bc4-c4e6342022b0.png?resizew=257)
(1)在
的条件下,将此枕木翻转90°(即宽度变为了厚度),枕木的安全负荷会发生变化吗?变大还是变小?
(2)现有一根横截面为半圆(半圆的半径为R=
)的柱形木材,用它截取成横截面为长方形的枕木,其长度即为枕木规定的长度l,问横截面如何截取,可使安全负荷最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/5/edf9e7aa-06e6-4f60-9bc4-c4e6342022b0.png?resizew=257)
(1)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e98454c36866188e748733a67f294a.png)
(2)现有一根横截面为半圆(半圆的半径为R=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2016-12-03更新
|
422次组卷
|
2卷引用:2016届山东省潍坊中学高三上学期开学考试理科数学试卷
10 . 定义在R上的奇函数
,当
时
恒成立,若
,
,
,则
的大小关系为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315d163a904f7034577a18cc1a33f871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee0a69d5a76b0bf5280d2f2931da3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572e4004017446004f6d2a6a60c93fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c516abfe63005efaade4f3f3cdb91e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7554bc202bb59e43b8525cf1b423dc0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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