问题 解答题
设函数f(x)=ax3+bx2+cx+d(a、b、c、d∈R)满足:对于任意的x∈R都有f(x)+f(-x)=0,且x=1时f(x)取极小值-
2
3

(1)f(x)的解析式;
(2)当x∈[-1,1]时,证明:函数图象上任意两点处的切线不可能互相垂直:
答案

(1)因为,∀x∈R,f(-x)=-f(x)成立,所以:b=d=0,

由:f'(1)=0,得3a+c=0,由:f(1)=-

2
3
,得 a+c=-
2
3
,解之得:a=
1
3
,c=-1从而,

函数解析式为:f(x)=

1
3
x3-x

(2)由于,f'(x)=x2-1,

设任意两数x1,x2∈[-1,1]是函数f(x)图象上两点的横坐标,

则这两点的切线的斜率分别是:k1=f'(x1)=x12-1,k2=f'(x2)=x22-1

又因为:-1≤x1≤1,-1≤x2≤1,所以,k1≤0,k2≤0,得:k1k2≥0知:k1k2≠-1

故当x∈[-1,1]是函数f(x)图象上任意两点的切线不可能垂直

完形填空

I got my first real job when I was ten.My dad,Benjamin,injured his back when working in a cardboard-box factory and was retrained as a hairstylist.He   1  space in a little strip mall and gave his shop the fancy   2  of Mr.Ben’s Coiffure.The owner of the shopping center gave Dad a on his rent for cleaning the parking lot three  4  a week,which meant getting up at 3 am.To  5   rubbish,Dad used a little machine that looked like a lawn mower.Mom and I  

garbage cans and picked up litter by hand.   7  took two to three hours to clean the lot.I’d  8

in the car on the way home.

I did this for two years,  9 the lessons I learned there have lasted a lifetime.I  10 discipline and a strong work ethic,and learned at an early age the importance of   11  life’s competing interests —in my case,school, homework and a job.This really 12 during my senior year of high school,   13    I worked 40 hours a week flipping (翻动) burgers at a fast-food joint while 14 a full load of college-prep courses.

The hard work   15  off.I attended the US Military Academy and went on to  16   graduate degrees in law and business from Harvard. Later,I   17  a big Los Angeles law firm and was elected to the California State Assembly.In these  18  and in everything else I’ve done,I have never forgotten those nights in the parking lot.The    19  taught me that there is dignity in all work and that if people are working to   20  for themselves and their families,that is something we should honor. 

1. A.bought           B.had          C.rented                         D.built

2. A.sign               B.mark         C.name                   D.board

3. A.discount         B.bill        C.praise                  D.punishment

4. A.days               B.hours         C.mornings             D.nights

5. A.make up           B.fill up    C.pick up                     D.take off

6. A.emptied                 B.collected C.carried                   D.filled

7. A.This               B.That      C.I                   D.It

8. A.cry                        B.laugh    C.complain               D.sleep

9. A.though                  B.but       C.so                   D.then

10. A.acquired              B.wanted        C.liked                   D.called

11. A.gaining                B.balancingC.avoiding            D.abandoning

12. A.worked                B.did      C.happened                     D.helped

13. A.then                    B.when     C.while                   D.as

14. A.having                 B.joining    C.taking                 D.doing

15. A.paid                    B.took      C.laid                     D.kicked

16. A.ask                  B.seek     C.accept                    D.receive

17. A.went                    B.joined     C.opened                D.charged

18. A.ways                   B.jobs      C.schools               D.firms

19. A.lessons                 B.memoryC.experience                  D.teachers

20. A.support                B.earn      C.give                           D.provide

单项选择题