题干

已知函数f(x)=x3﹣x+2 x .

(Ⅰ)求函数y=f(x)在点(1,f(1))处的切线方程;
(Ⅱ)令g(x)=
a
x
2
+
a
x
f
(
x
)
−
2
x
+lnx,若函数y=g(x)在(e,+∞)内有极值,求实数a的取值范围;
(Ⅲ)在(Ⅱ)的条件下,对任意t∈(1,+∞),s∈(0,1),求证: g(t)−g(s)>e+2−
1
e
.
上一题 下一题 0.0难度 选择题 更新时间:2018-05-18 11:10:23

答案(点此获取答案解析)

解:(Ⅰ)∵f(1)=13﹣1+2×1=2.

f′(x)=3x2−1+

同类题1

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    Of the many unpleasant emotions we can experience, fear may top the list. ____. Fear can also keep us from pursuing the things in life that really matter — like following our dreams, and developing important relationships. I have some ideas, though, of how to be free from fear.

Experience fear.

I used to be very afraid of speaking in front of people. I would get sweaty palms and my stomach would be so tied up that I wouldn't be able to eat. However, each time I spoke, I noticed afterwards that it wasn't that bad. Things I fear are never as bad in reality as I make them out in my mind. ____.

Create space.

    The first and most important step to being fearless is to create some space between ourselves and the emotion of fear. This isn't accomplished by ignoring the fear, or trying to talk ourselves out of it. ____. In fact, a recent research shows that by simply admitting the emotion we actually begin to reverse the "fight or flight(逃避)" response in the body.

Control the breath and feel the fear.

    Once we acknowledge the presence of fear, the second step is to control the breathing so that it becomes slower and gentler. We try to make the breath just a little bit longer, and feel how fear manifests(展现) in the body. ____.

    With practice, we can create enough space between us and the emotion of fear so that we're able to replace a fearful thought with a positive one. ____. For instance, before I get up to speak in front of a group of people, I imagine that the audience is positively impressed by what I say and that I manage to complete the speech successfully.

A. Space is created only when we can honestly acknowledge that fear exists.

B. We can imagine a positive outcome for whatever we're about to do.

C. Fear, if left uncontrolled, can even destroy our life.

D. So one way to get rid of fear is to simply push ourselves to do things that we fear.

E. When we can see a positive outcome in our mind, fear no longer holds us back.

F. But fear is more than just physically unpleasant.

G. As we pay attention to the physical symptoms of fear, we can see fear objectively.

同类题4

阅读理解

Tuesday,13th September

    I arrived in New York two weeks ago.I am writing my diary(日记)in English because my English teacher Rachel says it is a good way to practise English.So far, I like New York and my school.I have three classes a day.Most of my classmates come from Japan,South Korea,Spain,Germany and Australia.There aren't many Chinese students.so I have to use English most of the time.I am learning a lot!I am living in student housing,and I have my own comfortable room.

Thursday.20th October

    My English is hopeless!I was on the bus this morning and a man spoke to me,but I couldn't understand him.I was so embarrassed(尴尬的).Why is my English improving so slowly?I want to make lots of American friends,but this isn't happening so easily.I'm a shy girl.It is hard for me to talk to some people,even my classmates!I like them,but sometimes I can't understand them very well.I think I'm feeling homesick(想家的).I miss my friends and family.

Thursday.27th October

    I went to a school party last Friday and it was great.I talked with a Japanese boy named Kenji,a German girl named Wendy and an Italian girl named Carla.We talked about our countries' customs (风俗)and our experiences in America so far.We are going to walk around New York together this weekend.Also, Kenji wants me to write for the student newspaper here at school.Maybe things are getting better!

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