搜题请搜索小程序“爱下问搜题”
问题 填空题
若函数f（x）定义域内有两个任意实数x1，x2，满足f(
x1+x2
2
)＜
f(x1)+f(x2)
2
，则称函数f（x）为凸函数，下列函数中是凸函数的为 ______．
①f（x）=3x+1，②f(x)=
1
x
x∈（-∞，0），③f（x）=x2-3x-2，④f（x）=-|x+1|
答案

①

f(x1)+f(x2)
2
-f(
x1+x2
2
)=
3x1+1+3x2+1
2
-3
x1+x2
2
+1=0，不是凸函数；

②

f(x1)+f(x2)
2
-f(
x1+x2
2
)=
1
x1
+
1
x2
2
-
1
x1 +x2
2
=
2(x1-x2) 2
(x1 +x2) x1x2
符号不确定，故不为凸函数

③

f(x1)+f(x2)
2
-f(
x1+x2
2
)=
x12-3x1-2+x22-3x2-2
2
-(
x1+x2
2
)2+3
x1+x2
2
+2

=(

x1-x2
2
)2＞0，故为凸函数．

④

f(x1)+f(x2)
2
-f(
x1+x2
2
)=
-|x1+1|-|x2+1|
2
+|
x1 +x2
2
+1|，

取x1=1，x2=2则上式为0，故不是凸函数．

故答案为：③

阅读理解

Every year, the French town of Menton hosts an event called the Lemon Festival in the world. The Lemon Festival usually takes place between mid-February until March. During the festival, around 145 tons of oranges and lemons are sent into the town. Over 300 workers work together to make giant sculptures(雕塑) out of fruits.

Menton became the first producer of lemons in 1929. The lemons are loved by the world’s best cooks. In the late 19th century, a town parade was held to encourage Menton’s winter tourism. Kings, princes and artists filled the great and comfortable hotels or their own fantastic houses. Because of its great success, the streets were beautifully planted with oranges and lemons in the following years. In order to develop tourism, in 1934 the Lemon Festival was officially born.

Sleepy Menton becomes a world of color during the festival time. People find it very exciting and full of fun. The festival is enjoyed for three whole weeks. Along with a daily Lemon and Orange Exhibition, parades on Sundays, fireworks on Thursday nights.

Every year there will be a special theme for the Lemon festival. This year the theme of the Lemon Festival is: “The regions of France”. Some of the events are free, but you need to buy tickets to see the parades.

小题1:Why was the Lemon Festival officially born?

A．To encourage people to plant more lemons.

B．To help people enjoy the winter months.

C．To develop winter tourism in Menton.

D．To cerebrate the success of orange planting.小题2:What is the writer trying to tell us in the second paragraph?

A．The history of Menton.

B．The tourist attractions in Menton.

C．The special taste of the lemons in Menton.

D．The history of the Lemon Festival.小题3:You can enjoy the following activities EXCEPT_______ during the Lemon Festival.

A．lemon and orange shows

B．a town parade

C．fireworks

D．a concert小题4:In which part of a newspaper can you find the passage?

A．Travel

B．Family

C．Advertisement

D．Sport
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单项选择题

女性，68岁。患慢性支气管炎，肺气肿12年。2天前剧咳后，突然感到左侧胸痛伴呼吸困难，不能平卧。最可能的诊断是（）

A.肺炎

B.肺栓塞

C.心肌梗死

D.自发性气胸

E.结核性胸膜炎
查看答案