题目
题型:不详难度:来源:
(1)当a=1时,求函数f(x)的单调区间与极值;
(2)是否存在实数a,使f(x)的最小值是3?若存在,求出a的值;若不存在,说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-29111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-80780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-96943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-96943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-82958.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-38450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-52957.png)
令f′(x)>0,得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-51321.png)
f′(x)<0,得0<x<
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-51321.png)
∴f(x)的单调增区间是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-29111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-80780.png)
∴f(x)的极小值为f
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-59413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-96943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-51321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-96943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-96943.png)
(2)假设存在实数a,使f(x)=ax2-ln x,x∈(0,e]有最小值3,
f′(x)=2ax-
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-38450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-13718.png)
①当a≤0时,x∈(0,e],所以f′(x)<0,所以f(x)在(0,e]上单调递减,
∴f(x)min=f(e)=ae2-1=3,a=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-93266.png)
②当a>0时,令f′(x)=0,得x=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-70638.png)
(ⅰ)当0<
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-70638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-35712.png)
f(x)在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031149-15944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031149-11372.png)
∴f(x)min=f
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031149-93109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031146-96943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-70638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-82958.png)
(ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-70638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-35712.png)
所以f(x)在(0,e]上单调递减,
∴f(x)min=f(e)=ae2-1=3,a=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031148-93266.png)
综上,存在实数a=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031147-82958.png)
核心考点
试题【已知函数f(x)=ax2-ln x,x∈(0,e],其中e是自然对数的底数,a∈R.(1)当a=1时,求函数f(x)的单调区间与极值;(2)是否存在实数a,使f】;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/20191018/20191018031136-28077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-16499.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-52352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-27679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-52352.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-52352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-32744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-63049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-52352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031137-23831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031136-63049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031115-45690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031116-43763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031116-34272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031116-94742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031116-73915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031116-66660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031116-73915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-41509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-51737.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-51737.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-51737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-15119.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-81520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031118-51135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031118-51583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031117-81520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031118-70815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031100-37097.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031100-66710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031100-91486.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031100-54539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031100-51693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031048-96507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031048-72946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031048-10281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031049-62598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031049-82160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031049-63202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031049-54606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031050-74130.png)
(1)求切线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031049-63202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031050-32492.png)
(2)设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031050-66746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031050-13656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031050-35307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031051-33172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031033-94069.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031033-31656.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031034-90588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031034-24760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031034-61192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018031034-74185.png)
最新试题
- 1The old house, in front of _________ there is an apple tree,
- 2(12分)阅读下列材料,并回答:2007年10月15日上午举世瞩目的中国共产党第十七次全国代表大会在人民大会堂开幕,胡锦
- 3(2009湖南四校联考)The film company has given up idea of acti
- 4用毫米刻度尺测量物体的长度,下列哪些读数符合有效数字要求 ( )A.1.502mB.1.6214mC.12.40cmD
- 5“化疗”是控制癌细胞增殖的方法之一,药物可以***死癌细胞。下图是一个典型的化疗过程,每3周给药1次(图中箭头所示),图中记
- 6如图在平面直角坐标系xOy中,函数(x>0)的图象与一次函数y=kx﹣k的图象的交点为A(m,2).(1)求一次函数的解
- 7作图:(6分)(1)在图1中画出△ABC关于点O的中心对称图形。(2)正方形网格中,每个小正方形的顶点称为格点,以格点为
- 8如图,在长方体ABCD-A1B1C1D1中,AB=BC=2,AA1=1,则AC1与平面A1B1C1D1所成角的正弦值为
- 9下列说法正确的是( )A.发达国家大部分位于南半球B.发展中国家大部分位于南半球和北半球的南部C.发达国家之间有关经济
- 10完形填空。 School students in China have been learning dance
热门考点
- 1将直线y=x向上平移2个单位后,得到的直线的解析式是______;如果一条直线与直线y=x平行且过点(0,-3),则这条
- 2小明和小聪同学完成“装满水的杯子里还能放多少大头针”的实验后,交流讨论:放入大头针的数量多少与哪些因素有关?两人根据生活
- 3下列划线的字词注音不正确的一项是 [ ]A.视其缶(fǒu)谨食(sì)之殚(dā
- 4There was a big hole in the road which ___ the traffic.
- 5如果a是方程x2-3x+m=0的一个根,-a是方程x2+3x-m=0的一个根,那么a的值等于[ ]A.1或2B.
- 6Rose usually wakes up early in the morning. She always has h
- 7某女子是白化病基因携带者(Aa),有可能不含该致病基因的细胞是( )A.肌肉细胞B.神经细胞C.卵细胞D.口腔细胞
- 8不合理的农业生产活动会造成生态环境质量下降,如西北地区严重的水土流失。
- 9如图,在△ABC中,AC=16cm,AB的垂直平分线交AC于D,如果BC=10cm,那么△BCD的周长是 _______
- 10随着科学的发展,科学家们合成了一些氙的化合物。请回答下列问题。(1)Xe原子的价电子排布式为_________。稀有气体