题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113436-85760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113436-36706.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-86519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-89581.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
(3)若在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-33663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-52043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-46491.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-89581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-95378.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-47586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-98572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-41570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-51276.png)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-98536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-69841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-62162.png)
综上所述
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-69841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-62162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-98572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-41570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-51276.png)
(Ⅲ)(
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-81835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-23654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-83316.png)
解析
(1)先求解函数定义域和导数,然后得到切点处的导数值即为切线的斜率,利用点斜式得到方程。
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113441-61803.png)
(3)构造新的函数设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113441-77471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113441-42035.png)
解:(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113441-52758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113441-61803.png)
∴ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-86519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113442-86700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113442-27784.png)
∴ 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-89581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-95378.png)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113442-16245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113442-89856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113442-13552.png)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-47586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-98572.png)
![]() | (-1,0) | 0 | (0,![]() | ![]() | (![]() |
![]() | + | 0 | - | 0 | + |
![]() | ![]() ![]() | 极大值 | ![]() ![]() | 极小值 | ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-41570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-51276.png)
③ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-98536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-69841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113437-39301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-62162.png)
综上所述
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-69841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-62162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-98572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-41570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113439-51276.png)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113444-48059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113441-42035.png)
对
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113444-89821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113445-40207.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113445-90102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113436-85760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113445-36313.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113444-89821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113445-35586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113445-37688.png)
依题意,只需
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113446-34885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113446-67156.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113446-78965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113446-33421.png)
则正实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113438-46491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-81835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-23654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113440-83316.png)
核心考点
试题【(本小题满分12分)已知,函数(1)当时,求函数在点(1,)的切线方程;(2)求函数在[-1,1]的极值;(3)若在上至少存在一个实数x0,使>g(xo)】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113424-89308.png)
(Ⅰ)当a=﹣2时,求函数f(x)的单调区间;
(Ⅱ)若g(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113425-57620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113425-15281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113425-61713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113417-13673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113417-91653.png)
(Ⅰ)若a=1,求函数f(x)的极值;
(Ⅱ)若函数f(x)在区间[1,2]上为单调递增函数,求实数a的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113357-20523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113357-21516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113358-86428.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113358-30627.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113358-32108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113358-30627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113358-93740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113359-33393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113359-88939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113358-30627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113359-71114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113359-22097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113359-95119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113400-59446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113350-15415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113350-91827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113350-92870.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113350-98065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113350-55799.png)
在(-∞,-2)上为减函数.
(1)求f(x)的表达式;
(2)若当x∈
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018113340-54883.png)
(3)是否存在实数b使得关于x的方程f(x)=x2+x+b在区间[0,2]上恰好有两个相异的实根,若存在,求实数b的取值范围.
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