设a∈R,函数f(x)=((e^-x)/2)(ax^2+a+1),其中其中e是自然对数的底数.①判断f(x)在R上的单调性②判断f(x)在R上的单调性当-1＜a＜0时,求f(x)在[1,2]上的最小值

来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/25 08:53:41
设a∈R,函数f(x)=((e^-x)/2)(ax^2+a+1),其中其中e是自然对数的底数.①判断f(x)在R上的单调性②判断f(x)在R上的单调性当-1＜a＜0时,求f(x)在[1,2]上的最小值

设a∈R,函数f(x)=((e^-x)/2)(ax^2+a+1),其中其中e是自然对数的底数.①判断f(x)在R上的单调性②判断f(x)在R上的单调性当-1＜a＜0时,求f(x)在[1,2]上的最小值
设a∈R,函数f(x)=((e^-x)/2)(ax^2+a+1),其中其中e是自然对数的底数.
①判断f(x)在R上的单调性
②判断f(x)在R上的单调性当-1＜a＜0时,求f(x)在[1,2]上的最小值

设a∈R,函数f(x)=((e^-x)/2)(ax^2+a+1),其中其中e是自然对数的底数.①判断f(x)在R上的单调性②判断f(x)在R上的单调性当-1＜a＜0时,求f(x)在[1,2]上的最小值
(1）当a不等于0时.对f(x)求导得
f(x)’=（-0.5e^-x)(ax^2-2ax+a+1),令f(x)’=0所以f(x)’=（-0.5e^-x)(ax^2-2ax+a+1)=0 设K(x)=-0.5e^-x可知K(x)＜0
且在R上单调递增.又设H(x)=ax^2-2ax+a+1=0
由△=4a^2-4a（a+1)讨论得,《1》当△＞0时,a＜0即f(x)’=0的两根为(a+（-a)^0.5)/a和
（a-(-a)^0.5)/a.所以当x∈【-∞,(a+（-a)^0.5)/a】时f(x)’＞0即此时f(x)单调递增.当x∈【(a+（-a)^0.5)/a,（a-(-a)^0.5)/a】时f(x)’＜0即此时f(x)单调递减.当x∈【（a-(-a)^0.5)/a,+∞】时f(x)’＞0即此时f(x)单调递增.《2》当△＜0时f(x)’＜0即此时f(x)在x∈R上单调递减.
当a=0时,f(x)=0.5e^-x可知f(x)在x∈R上单调递增.
（2）你根据a的范围去求x是范围.再看看（1）中a＜0时的单调区间看看当x在[1,2]时是否单调,如果单调就将x=1和x=2带入f(x)对求出的两个值比较大小,小的就是最小值.如果不单调就把在[1,2]内的极值点和x=1和x=2带入f(x)比较三个值的大小,最小的就是答案.
解的不好见谅!第二问我没时间给你往这写了.你按那个过程试着做做就有答案了.

,ghd hair
[标签:标题]
[标签:标题]
The corporate word is ruled by a strong brand image, where each and every product has to make its presence felt among the consumers. In case you are looking forwa...

全部展开

,ghd hair
[标签:标题]
[标签:标题]
The corporate word is ruled by a strong brand image, where each and every product has to make its presence felt among the consumers. In case you are looking forward to improve your brand image, do check out the promotional gifts that help you in improving brand name and sales in a perfect way. In order to create a magic spell on your consumers, Click Promo Gifts (www.clickpromogifts.co.uk) would help you with an exclusive range of promotional products and items that can enhance the brand image and clientele of an organisation. At Click Promo Gifts, one can check out various promotional gifts such as promotional pens, mugs, coasters, umbrellas, mouse mats, conference bags, folders, sticky notes,ghd, travel mugs, golf gifts,ghd, fridge magnets, USB products, clocks and other desktop items that create a positive impact upon the clients. A good promotional gift helps a company in improving its client association and speaks well of its business practices along with creating goodwill. Promotional gifts and accessories are affordable medium of brand management in comparison to television and billboard advertisements that demand a huge investment. Given this advantage, promotional gifts can be procured in large numbers and distributed among clients and workers. Promotional gifts as giveaway gifts can be distributed during festivals, corporate meetings, trade shows and umpteen other instances so as to create good consumer relationship. With the distribution of promotional gifts, an organisation benefits from the increased publicity that builds brand awareness and brand visibility among customers. So, the best way to spell your magic among consumers is the use of promotional gifts. Promotional gifts that are used on daily basis unconsciously remind the consumer about the brand and help in promoting its goods and services in its own. Promotional items and gifts are the best way to create a direct marketing campaign so as to create a lasting impact on the consumers. At Click Promo Gifts, you can choose the promotional gift of your choice and help your organisation in improving its sales in a remarkable way. With the affordable promotional gifts,ghd IV Styler, one can keep a tab on the promotional expenses and help the products in getting noticed in a short duration of time. If one is planning to launch a new product,cheap ghd, promotional gifts are the best way to enhance its image by distributing freebies in trade fairs. Promotional products can work wonders for any organisation, given its advantage over other medium of promotional techniques. So get started with promotional gifts and enjoy increasing sales and growth rate with exquisite promotional products. For more information about promotional products, log on to www.clickpromogifts.co.uk. Give the promotional campaign a competitive edge with perfect promotional gifts and accessories from Click Promo Gifts.
More articles related to topics：


ghd 51_3848

51_2353

ghd 51_4296

收起

设随机变量X的密度函数f(x)=e^(-α|x|)/(2a),x∈R,求EX,DX 设a∈R,函数f（x）=(x^2-ax-a)e^x.求函数f(x)在[-2,2]上的最小值. 设a∈r,函数f【x】=lnx-ax 设a∈R,函数f(x)=e^-x/2(ax^2+a+1),其中e是自然对数的底数,f'(x)等于多少? 设函数f(x)=x(e^x+ae^-x)(x属于R）是偶函数,则实数a为? 设a∈R,若函数f(x)=e^x-ax,x∈R有大于零的极值点,则a的范围 高中数学函数题 设a∈R,函数f(x)=e^-x(x^2+ax+1),其中e是自然对数的底数.(1)讨论函数f(x)在R上的单调性；(2)当-1 设a∈R 求函数f（x）=e^-x(a+ax-x²)（e为自然对数的底数）的单调区间与极值 设函数f(x)=x^2+|x-a|+1x∈R求函数f(x)的最小值 设函数f（x）=x（e^x+ae^-x） （x∈R）是偶函数,则实数a的值为? 设a﹥0,f(x)=e^x/a +a/e^x是R上的偶函数.证明f(x)在（0,正无穷大）上是增函数 设函数f(x)=e^x(ax^2-x-1)a属于R 若f(x)在R上单调递减,求a的取值范围 设函数f(x)=ax³-3x²(a∈R),且x=2是y=f(x)的极值点.求函数g(x)=e^x·f(x)的单调区间. 设函数f(x)=ax^2+|x-a|+1x∈R求函数f(x)的最小值 设f（x）=e^x+ae^-x a∈R x∈R 讨论函数g(x)＝xf(x)的奇偶性 (2)若g设f（x）=e^x+ae^-x a∈R x∈R 讨论函数g(x)＝xf(x)的奇偶性 (2)若g(x)是个偶函数 解不等式f(x∧2-2)≤f(x) 设函数f(x)=x（e·+ae-·）PS·代表x次方,是偶函数,X∈R,求a? 设a∈R,函数f(x)=x²+ax+4(1)解不等式f(x)+f(-x) 设定义在实数集R上的函数,f(x)=(e^x/a)+(a/e^x) (1) f(x设定义在实数集R上的函数,f(x)=(e^x/a)+(a/e^x)(1) f(x)可能是奇函数吗?为什么?(2) 若f(x)是偶函数,试研究单调性.