题干

已知函数 f(x)=2lnx+x2﹣ax.

(Ⅰ)当a=5时,求f(x)的单调区间;

(Ⅱ)设A(x1,y1),B(x2,y2)是曲线y=f(x)图象上的两个相异的点,若直线AB的斜率k>1恒成立,求实数a的取值范围;

(Ⅲ)设函数f(x)有两个极值点x1,x2,x1<x2且x2>e,若f(x1)﹣f(x2)≥m恒成立,求实数m的取值范围.

上一题 下一题 0.0难度 选择题 更新时间:2017-08-07 04:53:43

答案(点此获取答案解析)

解:(Ⅰ)当a=5时,f(x)=2lnx+x2﹣5x.求导,

f′(x)= 2x2−5x+2x

同类题1

阅读理解

    Are you sick of going to bed late and waking up tired? Then grab your hiking boots and a tent. A new study suggests that camping in the great outdoors for a couple of days can reset your body clock and help you get more sleep.

    The body clock is an internal system that tells our bodies when it's time to go to sleep and when it's time to wake up. Scientists track this clock by measuring the amount of melatonin (褪黑激素) circulating in a person's blood at any given time.

    In a healthy sleeper, melatonin levels rise a few hours before bedtime, stay high through the night, and then settle back down when it's time to wake up.

    In our modern society, however, most of us stay up many hours past sunset and would probably sleep in many hours after sunrise if we could. And the trouble is, your melatonin levels may still be high when your alarm clock goes off in the morning, which leads to fatigue. It may also have other health consequences as well, such as diabetes (糖尿病), overweight and heart disease.

    Professor Kenneth Wright of the University of Colorado in the US wanted to see if our body clocks can be reset by a short stay in nature. His team recruited (招募) fourteen physically active volunteers in their 20s and 30s. Nine went on a weekend camping trip, while the other five stayed home. At the end of the weekend, the researchers reported that in just two days, the campers' body clocks had shifted so that their melatonin levels began to rise more than an hour earlier than they did before they left on the trip. By contrast, the body clocks of the group that stayed home shifted even later over the course of the weekend.

    “This tells us we can reset our clocks fast,” Wright said.

    Therefore, if you want to change your sleep patterns you could try to increase your exposure to natural light during the day and decrease the amount of artificial light you see at night. And if that doesn't work,there's always camping.

同类题3

中国近代史是一部屈辱的历史,列强的侵略使中国一步步沦为半殖民地半封建社会的深渊。阅读下列材料,回答后面的问题。 
材料一:中国是经历了深重苦难的国家,在工业革命发生前的几千年时间里,中国经济、科技、文化一直走在世界的第一方阵之中。近代以后,中国的封建统治者夜郎自大,闭关锁国,导致中国落后于时代发展步伐,鸦片战争则成为中国历史的一块界碑。
——***2014年4月1日在比利时布鲁日欧洲学院的演讲
(1)发动鸦片战争的是哪一国家?这场战争签订了什么条约?
(2)“鸦片战争成为中国历史的一块界碑”的原因是什么?
材料二:在距“1894年中日事件”120年后的2014年4月21日,日本首相安倍晋三向靖国神社供奉祭品。靖国神社是日本军国主义对外侵略的精神支柱,其中供奉着近代以来历次战争中战死的日军亡灵,包括二战时对中国和周边国家犯下滔天罪行的战犯。
——新华网
(3)材料二中的“1894年中日事件”指什么?用一句话概括“1894年中日事件”对中国造成的重大影响。
材料三:清国之败,非君相一己之罪,盖其墨守常经,不变通所致也。夫取士必考试,考试必由文艺,文艺乃为显荣之阶梯,岂足济实效乎?……前三十载,我日本之国事,遭若何等之辛酸,厥能免于垂危者,度阁下之所深悉也。当此之时,我国去旧治,因时制宜,更张新政,为国可存立之一大要图。
——摘编自1895年《大日本海军总司令官伊东佑亨致大清国北洋水师提督丁汝昌书》
(4)依据材料三并结合所学知识,分析归纳甲午中日战争双方胜与败的原因分别是什么?
材料四:清政府赔偿白银4.5亿两,以海关等税收作担保;清政府保证严禁人民参加反帝活动;清政府拆毁大沽炮台,允许帝国主义国家派兵驻扎北京到山海关铁路沿线要地;划定北京东交民巷为使馆界,允许各国驻兵保护,不准中国人居住。
——摘自北师大版教材八年级上册《历史》
(5)材料四的内容出自哪一条约?该条约是在哪次战争后签订的?条约签订后,中国的社会性质发生了怎样的变化?
(6)从中国近代的屈辱史中,你获得什么感悟?