问题 解答题
已知函数f(x)=
3
x-1
(x∈[2,6]).试判断此函数在x∈[2,6]上的单调性并求函数在x∈[2,6]上的最大值和最小值.
答案

设x1、x2是区间[2,6]上的任意两个实数,且x1<x2

f(x1)-f(x2)=

3
x1-1
-
3
x2-1

=

3[(x2-1)-(x1-1)]
(x1-1)(x2-1)

=

3(x2-x1)
(x1-1)(x2-1)

由2≤x1<x2≤6,得x2-x1>0,(x1-1)(x2-1)>0,

于是f(x1)-f(x2)>0,即f(x1)>f(x2).

所以函数f(x)=

3
x-1
是区间[2,6]上的减函数.

因此,函数f(x)=

3
x-1
在区间的两个端点上分别取得最大值与最小值,

最大值f(2)=3,最小值f(6)=

3
5

阅读理解

Penguins live together,but each pair has a little piece of ground of their own.When a penguin wants to walk through its neighbor’s ground,it must ask permission.If it does not do that,it will have to fight.Most of the time,penguins live on the water.They eat shell fish and look after their children carefully.

All penguins are good parents—the male penguins are perhaps the best parents in the world. They walk in the sea in the middle of the dark Antarctic water. They choose their wives in the dark.They can only hear them—not see them.Then the female penguins lay their eggs and go away for about two months.The males take care of the eggs.If the eggs get cold,there will be no chicks.There is no food.The snow falls heavily and the wind blows strongly—sometimes at 150 kilometers an hour.The penguins do not move.When the females return from the sea,they will not remember their husbands.It does not matter.Only one thing matters—the eggs.Male penguins never fight—unless a penguin leaves a chick for a minute.They then fight because they all want it.They are strange and wonderful birds.

小题1:It seems interesting and unusual that the male penguins choose their wives ______.

A.when the female penguins return from the sea

B.just by hearing in the darkness

C.each time they see the lovely females

D.after they have had their own grounds小题2:Male penguins fight when ______.

A.they choose their wives

B.they see a chick left alone

C.they want to get something to eat

D.they walk through their neighbors’ ground小题3:From the passage we know that ______.

A.penguins live a hard life

B.penguins live in pairs

C.penguins will fight if one walks through others’ ground without permission

D.each penguin has a little piece of ground of its own小题4:The penguins choose their wives in the dark. We can infer that ______.

A.penguins like nights very much

B.there is no daytime in that place at all

C.the weather is cloudy and rainy all the year around

D.the sun can’t shine there for nearly half a year every year小题5:Which of the following is NOT true?

A.Female penguins take care of the eggs.

B.Female penguins often have their new husbands.

C.Male penguins use their ears to choose wives.

D.Male penguins don’t move when they take care of eggs,even though the wind often blows strongly.

单项选择题