问题 解答题

函数y=a2x+2ax-1(a>0且a≠1)在区间[-1,1]上有最大值14,试求a的值.

答案

令b=ax则a2x=b2

∴y=b2+2b-1=(b+1)2-2   对称轴b=-1

若0<a<1,则b=ax是减函数,所以a-1>a

所以0<a<b<

1
a

所以y的图象都在对称轴b=-1的右边,开口向上 并且递增

所以b=

1
a
时有最大值

所以y=b2+2b-1=14∴b2+2b-15=0∴(b-3)(b+5)=0

b>0,所以    b=

1
a
=3,a=
1
3
符合0<a<1

若a>1则b=ax是增函数,此时0<

1
a
<b<a

y的图象仍在对称轴b=-1的右边,所以还是增函数

b=a时有最大值

所以y=b2+2b-1=14

b>0,所以b=a=3,符合a>1

所以a=

1
3
或a=3

阅读理解

阅读理解。根据短文内容,从A、B、C、D四个选项中选出最佳答案。

    The picture show eighteen-year-old Katy Ross in Nepal, small country in north India. Katy left school 8

months ago and soon she will go to university. She loves travelling and decides to visit Asia before she goes to

university.

    Katy is living with a family in the capital of Nepal. She has learnt a lot about the country since she arrived 4

months ago. The family has two children but many uncles and cousins live with them in their big house. They

have taken Katy to many parties.

    Katy teaches for four hours a day at a small school. All the classes are in English and the pupils have spoken

English since the age of six. The older children speak English very well. Katy has taught writing, grammar and

art, all in English. She enjoys art most. And she thinks the children like the lessons best, too.

    Katy has not a lot of time to see Nepal, but soon she will stop teaching and travel around Nepal with a friend.

"After that," Katy says, "we will visit more countries in Asia. We're not sure which ones yet."

1. Why is Katy in Nepal? [ ]

A. She is studying there.

B. She wants to take some pictures there.

C. She wants to learn more about the country.

D. She is an exchange student

2. Which of the following is TRUE about the family Katy is living with? [ ]

A. They are friendly.

B. There are three people in their house.

C. They are strange.

D. They have never taken Katy to the parties.

3. How long has Katy been in Nepal? [ ]

A. eight months

B. six months

C. four months

D. one moth

4. When did the children begin to speak English? [ ]

A. When they are 5 years old.

B. When they are 6 years old.

C. When they are 7 years old.

D. When they are 8 years old.

5. According to the passage, Katy __________________. [ ]

A. likes travelling very much

B. doesn't want to live with a family

C. only teaches writing in English

D. will go back to school after she leaves Nepal

问答题