问题 单项选择题

下列命题不正确的是
(A) 设(x0,f(x0))是曲线y=f(x)的拐点,又f"(x0)存在,则f"(x0)=0.
(B) 设f"(x0)=0,

,则(x0,f(x0))是曲线y=f(x)的拐点.
(C) 设f(x)在[a,b]上连续,在(a,b)内可导且为凸函数.若f(a)=f(b)=0,则f(x)>0(x∈(a,b)).
(D) 设函数f(x)、g(x)的图形都是凸的,那么函数f(x)·g(x)的图形也是凸的.

答案

参考答案:D

解析: 对于(A):由

在某U(x0,δ)可导,因(x0,f(x0))是拐点

在x0两侧凹凸性相反

在x0两侧单调性相反

是f’(x)的极值点.对f’(x)由费马定理得f"(x0)=0.故(A)正确.
对于(B):不妨设f(3)(x0)>0.由f(3)(x0)的定义及极限的不等式性质知


0<x-x0<δ时,f"(x)>0;-δ<x-x0<0时,f"(x)<0

在x=x0两侧f(x)的凹凸性相反.因此,(x0,f(x0))是y=f(x)的拐点.故(B)正确.
对于(C):参见图2-4,由罗尔定理得,

,f’(C)=0.由f(x)是凸的

在(a,b)单调下降



在[a,c]单调上升,f(x)>f(a)=0(x∈(a,c]),f(x)在[a,b]单调下降,f(x)>f(b)=0(a∈[c,b)).因此,f(x)>0(x∈(a,b)).故(C)也正确.
对于(D):例女口函数f(x)=g(x)=-x2,因f"(x)=g"(x)=-2<0,所以y=f(x),y=g(x)的图形都是凸的.若记h(x)=f(x)·g(x)=x4则由于h"(x)=12x2≥0可知y=h(x)=f(x)·g(x)的图形是凹的.故(D)不正确.
综上分析,应选(D).

阅读理解

阅读理解。

     Bowing is a very important custom in Japan. Unlike people in many other countries, they greet each other

by bowing instead of shaking hands. It is impolite not to return a bow to whoever bows to you.

     Bowing has many functions in one. It expresses the feeling of respect, thanks, regret, and so on. You can

bow when you say, "thank you", "sorry", "hello", "goodbye", "congratulations", "excuse me", "good morning",

and more.

     Bowing seems simple, but there are different ways of bowing. Bowing techniques vary from a small nod

of the head to a long, 90-degree bow. It depends on the social position or age of the person you bow to. If

your opposite is of higher social position or older than yourself, you are supposed to bow deeper and longer

than him or her. It is polite to bow from your waist. Men usually keep their hands at their sides, and women

usually put their hands together on their legs with their fingers touching. If it is not a very formal situation,

you can bow by nodding. The most common bow is a bow of about 15 degrees.

     You might feel strange doing it, but try to bow in Japan. You will be considered very polite!

1. The author writes the passage mainly to _____. [ ]

A. introduce the history of bowing in Japan

B. describe the purposes of bowing in Japan

C. introduce the Japanese custom of bowing

D. describe different ways of bowing in Japan

2. By saying "Bowing has many functions in one", the author means that _____. [ ]

A. people can express different feelings by bowing

B. one kind of bow has many similar functions

C. people bow to express their feelings

D. the more times you bow, the more respect you receive

3. How people greet in many countries? [ ]

A. by bowing

B. by shaking hands

C. by kissing each other

D. by touching

4. If an assistant wants to show respect to her professor, she may bow like _____. [ ]

A.

B.

C.

D.

单项选择题