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问题 解答题
已知函数f（x）=ax4+bx2+cx+1（a，b，c∈R），在x=-1处取得极值-
1
4
，在x=-2处的切线与直线x-8y=0垂直．
（1）求常数a，b，c的值；
（2）对于函数h（x）和g（x），若存在常数k，m，对于任意x∈R，不等式h（x）≥kx+m≥g（x）都成立，则称直线y=kx+m是函数h（x），g（x）的分界线，求函数f（x）与函数g（x）=-x2+2x+1的“分界线”方程．
答案

（1）f'（x）=4ax3+2bx+c，

由条件得到：

-4a-2b+c=0
a+b-c+1=-
1
4
-32a-4b+c=-8
，

得到：

a=
1
4
b=
1
2
c=2
（6分）

（2）依题意

1
4
x4+
1
2
x2+2x+1≥kx+m≥-x2+2x+1恒成立，

令x=0，则1≥m≥1，所以m=1，（8分）

因此：kx+1≥-x2+2x+1恒成立，即x2+（k-2）x≥0恒成立，

由△≤0得到：k=2，（10分）

又因为：f(x)-(2x+1)=

1
4
x4+
1
2
x2≥0，所以f（x）≥2x+1恒成立，

所以：函数f（x）与函数g（x）=-x2+2x+1的分界线方程是y=2x+1．（12分）

单项选择题

Text 2

The Boston Marathon is an annual marathon sporting event hosted by the city of Boston, Massachusetts, on Patriots’ Day, the third Monday of April. Begun in 1897 and inspired by the success of the first modem-day marathon competition in the 1896 Summer Olympics, the Boston Marathon is the world’s oldest annual marathon and ranks as one of the world’s most well-known road racing events. The marathon is one of five members of the World Marathon Majors.
The event attracts an average of about 20,000 registered participants each year. In the 100th running of the Boston Marathon in 1996, the number of participants reached 38,000. While there are cash prizes awarded to the winners of the marathon, most of the runners participate for the accomplishment of having run the race at all.
The Boston Marathon was originally a local event, but its fame and status have attracted runners from all over the world. For most of its history, the Boston Marathon was a free event, and the only prize awarded for winning the race was a wreath woven from olive branches. However, corporate-sponsored cash prizes began to be awarded in the 1980s, when professional athletes began to refuse to run the race without cash awards. The first cash prize for winning the marathon was awarded in 1986.
Women were not allowed to enter the Boston Marathon officially until 1972. Roberta (Bobbi) Gibb is recognized as the first woman to run the entire Boston Marathon (in 1966). In 1967, Kathrine Switzer, who had registered as "K. V. Switzer", was the first woman to run with a race number. She finished, despite a celebrated incident in which race official Jock Semple tried to rip off her numbers and eject her from the race. In 1996 the B.A.A. retroactively recognized as champions the unofficial women’s leaders of 1966 through 1971.
In recent years, critics have pointed to the dominance of foreign-born athletes in the event (especially runners from Kenya) to back their arguments that American professional running is lagging behind the rest of the world in terms of producing quality athletes. However, foreign dominance of the race is nothing new. Between 1946 and 1967 only one American (John J. Kelley in 1957) won the marathon in an era when Finland and Japan were the distance powerhouses.
The Boston marathon is open to all runners, male and female, from any nation, but they must meet certain qualifying standards. To qualify, a runner must first complete a standard marathon course certified by a national governing body affiliated with the International Association of Athletics Federations within a certain period of time before the date of the desired Boston Marathon (usually within approximately 18 months prior). Prospective runners in the age range of 18-- 34 must run a time of no more than 3:10:59 (3 hours and 10 minutes) if male, or 3:40:59 (3 hours and 40 minutes) if female; the qualifying time is adjusted upward as age increases. For example, a 40--44 year old male can still qualify with a time of 3:20:59. An exception to the qualification requirement is awarded to 1,250 runners who raise a pre-determined level of sponsorship for officially designated local charities.
Besides the Olympic trials and the Olympic marathons, Boston is the only major American marathon that requires a qualifying time. Thus for many marathoners to qualify for Boston (to "BQ") is a goal and achievement in itself, making it a "people’s Olympic event."

Why do people criticize that America can’t train better professional runners than some other countries

A．Because most winners of the race come from foreign countries.

B．Because only one American won the race between 1946 and 1967.

C．Because Finland and Japan were the p teams with quality athletes.

D．Because American professional running is far behind.
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多项选择题

GB/T24001-2004标准4.4.1条款规定（）

A、管理者应确保环境管理体系建立、实施、保持和改进提供的必要的资源

B、应对职责何权限作出明确规定并形成文件

C、资源只包括人力资源、财力资源、基础设施（条款：资源包括：人力资源、专项技能、基础设施、技术和财力资源）（有题目考：包括生产设备（错误）

D、管理者代表负有提出改进建议的职责
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