设函数
.
(1)求函数
的单调区间;
(2)若函数
有两个极值点
且
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e460df04c705d34f06ec92276f598025.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650e93028e040413ca1c378e02ecde2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5289aeb8d61821f7c734a4801ba86021.png)
更新时间:2018-01-04 09:28:42
|
相似题推荐
解答题-问答题
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解题方法
【推荐1】在线性回归是利用数理统计中回归分析,来确定两种或两种以上变量间相互依赖的定量关系的一种统计分析方法,运用十分广泛.回归分析中,只包括一个自变量和一个因变量,且二者的关系可用一条直线近似表示,这种回归分析称为一元线性回归分析.一般来说,线性回归都可以通过最小二乘法求出其方程,可以计算出对于
的直线.残差是真实值和预测值间的差值,对于一组数据
,其残差可以表示为
其中
为真实值,
为估计值对于我们数据中的每个点如此计算一遍,再将所有的
相加,就能量化出拟合的直线和实际之间的误差.其公式为:
.这个公式是残差平方和,对于回归直线的确定,普通最小二乘法给出的判断标准是:残差平方和的值达到最小.在数学中,处理多个参数的函数的极值时,我们可以采用偏导法,即单独对某个参数求导,将其他参数视为常数.根据以上信息,请推导公式:
,
,(其中
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef046c85a536174bec951a53d9f60b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812cd0da7560a55406a59d92e5f856dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd4a42766ee60fa7714de1006a5eb32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a74fcd84480a51dc805abc8a586b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b4f0cf535253536ddbfd517228bc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba989ca9a7c4410fe872b0dc08eecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40ea92b18e6a33485441818d471945f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57669f9af5ddd5ca466c11f472ea90e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2083ce194593322ffb0d746b4a41eb7d.png)
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【推荐2】若函数
的导函数
在点
可导,则称
在点
的导数值为
在点
的二阶导数,记作
.若
在开区间I内的每一点都二阶可导,则得到一个定义在I上的二阶导函数,记作
.曲线
上任意两点间的弧段总在这两点的下方;而曲线
则相反,任意两点间的弧段总在这两点连线的上方.我们把具有前一种特性的曲线称为凸的,相应的函数称为凸函数;后一种曲线称为凹的,相应的函数称为凹函数.连续曲线上凹弧与凸弧的分界点称为曲线的拐点.拐点在统计学,物理学,经济学领域都有重要的应用.若函数
在定义域内是一条连续不断的曲线,对任意的
,
的导函数
都存在,且
的导函数
也都存在,若
,使得
,且在
的左右附近,
异号,则称点
为曲线
的拐点.已知函数
,
,
.
(1)求
在定义域内的拐点个数;
(2)若
在
上有唯一拐点
,求实数k的取值范围;
(3)函数
在区间
恰有一个拐点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268ea7b6a873194253b75233ac18545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a09c048d8ea4456b9db662b39d3a208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd16646e695eeb7088134cb94d51691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559f5db9b978cb2bd290dbce7268629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2430fa48f248e998e256e91165970bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d74fb771e771f22b7e4249da06289e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a63eed6f348f10044c48dacb045b7b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3ac8b888cea3c2a212f4b21447d3bd.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2629d7ba67bc8caed81c64c3c1341275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
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解题方法
【推荐1】已知函数
,其中
为常数.
(1)当
时,求函数
在
上的值域;
(2)若
,设函数
在(0,1)上的极值点为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381621fd61d9b2e68f3a4c412c0021be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb49dbba01c4ff5f686ffc8828351b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ffe0afc6fa9e62ff75d13f656e7cc4.png)
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【推荐2】已知函数
,
.
(1)求证:
存在唯一零点;
(2)设
,若存在
,使得
,试比较
和
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a93f456f46d4d48ecf3792b2d816dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace5d9b3f07c5ac9e7aa736b948c17bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353c155779f27687a1f60eaa990eb61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e59990dd7e8a616f1f5a3f5b9ef022e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0392661557e18d4ec7d30ee53bbe8ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b88d4cca7070c3b237d35757d3b44c.png)
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【推荐1】已知函数
.
(1)当
时,讨论函数
的单调性;
(2)若方程
有两个不相等的实数根
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d70afb2987dec662121abd0313bfa02.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
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【推荐2】已知函数
.
(1)讨论
的单调性;
(2)若函数
在
上无零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf0acec1300b25bae04f531f14854d7.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐1】已知函数
.
(1)当
时,求
的单调递减区间;
(2)若
有两个极值点
,
(
).
①求实数b的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dcbfc01a30265d01acfa665daf72da3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/26d8dafc71b106f39f4e15442220897b.png)
①求实数b的取值范围;
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c1239e82dc69ad3f0f4eb27ac44d48.png)
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名校
【推荐2】设函数
,其中
.
(Ⅰ)若
,求曲线
在点
处的切线方程;
(Ⅱ)若函数
在
上有极大值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e927ec74fe8b14d660cca855583a4f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(Ⅰ)若
![](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/5bea9227dd0104da58e0c40952cc87ed.png)
(Ⅱ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f9f734c03d04c21edefa08e0acc1fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
【推荐3】已知函数
.
(1)求曲线
在点
处的切线方程;
(2)若函数
存在两个极值点
,
,求实数a的取值范围,并证明:
,
,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a5769abc37f20cad8961f5814bce80.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/dc9769116ec47353514e6b7fb7b17216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542893790445d6d888d9ff91fd215c9c.png)
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