题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014519-42814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014519-83051.png)
定义:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-24464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-26257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-22379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-87873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014521-65295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014521-12514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-26257.png)
定义:(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014521-65295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014521-78066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-26257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014521-51546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-25526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-26257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014521-12514.png)
己知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-59359.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-44432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-37138.png)
(2)检验函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-44432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-37138.png)
(3)写出一个三次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-96931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-32225.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-73036.png)
(2)一般地,三次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-23343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014519-83051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-17953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-44432.png)
或者:任何一个三次函数都有拐点;任何一个三次函数都有对称中心;任何一个三次函数平移后可以是奇函数.
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-62155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-60815.png)
解析
试题分析:(1)依题意,计算
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-18646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-53524.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-87873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-76400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-27725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-73036.png)
(2)由(1)知“拐点”坐标是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-73036.png)
根据定义(2),考查
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-44807.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-72536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-91165.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-71958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014526-65639.png)
作出结论:
一般地,三次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-23343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014519-83051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-17953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-44432.png)
或者:任何一个三次函数都有拐点;任何一个三次函数都有对称中心;任何一个三次函数平移后可以是奇函数.
(3)根据(2)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014526-28524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-62155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-60815.png)
试题解析:(1)依题意,得:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-18646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014526-14772.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014520-87873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014526-48690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-76400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-27725.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-59359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-73036.png)
(2)由(1)知“拐点”坐标是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-73036.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-44807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-72536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-91165.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014525-71958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014526-65639.png)
由定义(2)知:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014526-42988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-73036.png)
一般地,三次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-23343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014519-83051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-17953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014522-44432.png)
(或者:任何一个三次函数都有拐点;任何一个三次函数都有对称中心;任何一个三次函数平移后可以是奇函数 )都可以给分
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014527-31029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014523-62155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014524-60815.png)
核心考点
试题【对于三次函数。定义:(1)设是函数的导数的导数,若方程有实数解,则称点为函数的“拐点”;定义:(2)设为常数,若定义在上的函数对于定义域内的一切实数,都有成立,】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014503-39870.png)
(1)求函数f(x)的最小值;
(2)当a>0,且a为常数时,若函数h(x)=x[g(x)+1]对任意的x1>x2≥4,总有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014503-88182.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014503-93400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014503-17836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014452-65072.png)
(1)当a=3,b=-1时,求函数f(x)的最小值;
(2)若曲线y=f(x)在点(e,f(e))处的切线方程为2x-3y-e=0(e=2.71828 为自然对数的底数),求a,b的值;
(3)当a>0,且a为常数时,若函数h(x)=x[f(x)+lnx]对任意的x1>x2≥4,总有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014452-44305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014435-82768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014436-92725.png)
(1)讨论函数f(x)的单调性;
(2)若a=1,函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014436-43852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014436-45931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014425-42418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014425-13459.png)
(1)若函数在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014425-15772.png)
(2)如果当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014426-40617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014426-46245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014421-54137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018014421-54933.png)
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