Correct

极 vs 极端 vs 极其

/ jí vs jíduān vs jíqí /
Strokes

Formula

1
极 + 少数
2
极 + 个别
3
极 + 了

Definition

极 is an Adverb, 极端 is a Noun or an Adjective, and 极其 is an Adverb, which all means [extremely; extreme].

Example

极, 极端, 极其 all mean "extremely" when they are used as adverbial. 极 and 极其 are Adverbs and can only function as adverbials. 极端 is an Adjective but can also function as an adverbial.
1) 极, 极端, 极其 are seldom interchangeable because 极端 and 极其 mostly qualify as disyllabic words while 极 qualifies as monosyllabic words.

2) In the examples, if 极其 is used in example ④, one will say 极其富有特色. In example ⑤ 极其 can replace 极. In example ⑥ one can say 极其炎热.
1
Zhèzhǒng
这种
shāngpǐn
商品
  
(
极其
  
)
ángguì
昂贵
  

This commodity is very expensive.

2
li
那里
chǔ
地处
hándài
寒带
  
,
  
(
极其
  
)
hánlěng
寒冷
  

The place is in cold zone and it is very cold there.

3
duì
gōngzuò
工作
  
(
极其
  
)
rèn
责任
  

He is irresponsible for his job at all.

4
Zhè
piān
wénzhāng
文章
极富
特色
  

The article is unique.

5
Zhèxiē
这些
míngōng
民工
néng
chī
吃苦
  

These civilian workers are very industrious.

6
Zhè
这里
chǔ
地处
dài
热带
  
,
tiān
天气
  

The place is in tropical zone, and it is very hot.

极端 (Noun) only can be used and the verbs are limited to 走, 陷人, 陷于, etc., to mean "extreme" (with a derogatory sense) and used as an object.
7
ge
哥哥
dìng
一定
yào
zuò
liúlàng
流浪
shīrén
诗人
  
,
di
弟弟
dìng
一定
yào
dāng
shang
和尚
  
,
zhēnshi
真是
zǒu
de
duān
极端
  

The brother wants to be a mintel, while he lttle brother wants to be a monk. They really go to extremes.

8
men
我们
kàn
wèn
问题
yào
quánmiàn
全面
  
,
néng
zǒuduān
走极端
  

We should take a balanced point of view ——don't go to extremes.

极端 (Adjective) only can be used, to mean" very high degree" (with derogatory sense) functioning as the predicate.
9
men
他们
zhèzhǒng
这种
zuò
做法
tài
duān
极端
le
  
!

Their way is really in an extreme!

10
zěnme
怎么
zǒngshì
总是
zhème
这么
duān
极端
  
?
Nándào
难道
néng
wēn
温和
xiē
一些
ma
  
?

Why are you so radical? Why not be mild?

极端 (Adjective) only is used, with a nonpositive, extraordinary sense, to mean "very high degree", as an attributive.
11
shì
duān
极端
de
zhǔzhě
主义者
  
,
suǒ
所以
méiyǒu
没有
péngyou
朋友
  

He is acomplete individualist, so he has no friends.

12
biǎoxiàn
表现
chū
de
duān
极端
de
qíng
热情
  
,
zhēn
ràng
rén
shòuliǎo
受不了
  

Her enthusiasm is too much to be accepted.

13
zhèzhǒng
这种
duān
极端
xīngfèn
兴奋
de
zhuàngtài
状态
wèi
未必
利于
sài
比赛
  

Her extreme excitement does not necessarily do good to her match.

14
Zhè
shì
zhǒng
duān
极端
qíngkuàng
情况
  
,
suǒ
所以
yào
cǎi
采取
duān
极端
cuòshī
措施
  

This is an extreme that should be dealt with by responding measures.

极 only is used, to mean "a very high level", qualifying nouns of locality and a few words like 少数,个别, etc.
This is a special usage of 极.
极 + 少数 极 + 个别
15
tiáo
liú
河流
chǔ
地处
zhège
这个
shěng
de
nán
南部
  

The river flows in the southemmost part of the province.

16
Zhège
这个
chéngshì
城市
zài
guó
我国
běi
北部
  

The city lies in the northemmost part of our country.

17
Zhīyǒu
只有
shǎoshù
少数
ge
rén
tóng
同意
zhèzhǒng
这种
guāndiǎn
观点
  

Only a few people agree with the view.

18
Zhè
shì
zhǒng
bié
个别
de
qíngkuàng
情况
  
,
néng
shuōmíng
说明
wèn
问题
  

This is a special case, which cannot indicate the whole.

极 only is used, and often with 了, to mean "a very high level", used as a compliment.
极 + 了
19
Shān
山里
de
qiūtiān
秋天
měi
le
极了
  

The mountainous area is very beautiful in autumn.

20
Zuìjìn
最近
zhāngxiānsheng
张先生
máng
le
  

Mr. Zhang has been extremely busy recently.