
Thai: 
สมมุติว่า f ของ x เท่ากับ x คูณ e กำลังลบ
2x กำลังสอง และเราอยากหาจำนวนวิกฤตสำหรับ f
ผมแนะนำให้คุณหยุดวิดีโอนี้แล้วคือว่า
คุณหาจำนวนวิกฤตของ f ได้ไหม
ผมถือว่าคุณได้ลองแล้วนะ
ลองทบทวนกันหน่อยว่าจำนวนวิกฤตคืออะไร
เราบอกได้ว่า c เป็นจำนวน
วิกฤตของ f ก็ต่อเมื่อ
ผมจะเขียน iff ด้วย f สองตัว ย่อมาจาก
if and only if
f ไพรม์ของ c เท่ากับ 0 หรือ 
f ไพรม์ของ c ไม่นิยาม
ถ้าเราดูจำนวนวิกฤตสำหรับ f เราอยากหา

Czech: 
Řekněme, že f(x) se rovná x krát
e umocněné na (−2 krát (x na druhou)).
Chceme najít
stacionární body funkce f.
Zastavte si video a zkuste stacionární
body funkce f najít nejprve sami.
Předpokládám,
že jste to zkusili.
Zopakujme si,
co je stacionární bod.
Řekneme, že bod ‚c‘ je stacionárním
bodem funkce ‚f‘ tehdy a jen tehdy...
Napíšu jenom „iff“, což je
zkratka pro „tehdy a jen tehdy“.
...když je derivace funkce f v bodě ‚c‘
rovna 0, nebo není definována.
Když tedy hledáme stacionární body
funkce f, tak hledáme všechny body,

Portuguese: 
Digamos que f(x) é igual a x*exp(-2x^2), 
e queremos encontrar pontos críticos para f(x).
Eu então o encorajo a pausar este vídeo e pensar nisso,
você consegue encontrar algum ponto crítico para f(x)?
Assumo que você já tentou. Recordemos 
o que é um ponto crítico.
Digamos que c é um ponto crítico de f(x), se e somente se
-- e eu vou escrever "se" com dois s's (sse), 
a abreviação de "se e somente se"
f'(c) = 0 ou f'(c) é indefinido.
Então, se olharmos para os pontos críticos para f, 
queremos encontrar todos os lugares

Bulgarian: 
Нека да кажем, че функцията
 f от х е равна на
х по е на степен –2x^2,
и искаме да намерим 
критичните точки за функцията.
Насърчавам те да спреш 
видеото и да помислиш
дали можеш да намериш някакви 
критични точки за функцията f.
Предполагам, че вече 
го направи.
Нека само да си припомним
 какво означа критична точка.
Критична точка c 
наричаме такaва стойност на f,
тогава и само тогава –
записвам съкратено 
"тогава и само тогава" –
когато производната f' от с e равна 
на 0, или f' от с не е дефинирана.
Ако търсим критични точки за 
функцията f, то искаме да открием

Korean: 
함수 f(x)가 이렇게 주어져 있습니다
함수 f(x)의 극점을 찾을 것입니다
여러분이 이 영상을 잠시 멈추고
이 함수의 극점을 찾을 수 있는지
생각해 보기를 권장합니다
여러분이 한번 해볼 것 같은데요
극점이 무엇인지 한 번 상기시켜 봅시다
c가 f(x)의 임계점이라고 해봅시다
이 경우에 한해서
줄여서 if를 두개의 f로 쓰겠습니다.
f'(c)=0이거나
f'(c)는 정의되지 않을 것입니다
f(x)의 극점들을 찾을 때

English: 
Let's say that f of x is equal
to x times e to the negative
two x squared, and we want to
find any critical numbers for f.
I encourage you to pause
this video and think about,
can you find any critical numbers of f.
I'm assuming you've given a go at it.
Let's just remind ourselves
what a critical number is.
We would say c is a critical
number of f, if and only if.
I'll write if with two f's,
short for if and only if,
f prime of c is equal to zero
or f prime of c is undefined.
If we look for the critical
numbers for f we want to figure

Thai: 
ตำแหน่งทุกตัวที่อนุพันธ์ของมัน
เทียบกับ x เท่ากับ 0 หรือไม่ก็ไม่นิยาม
ลองคิดดูว่าเราหาอนุพันธ์ของฟังก์ชันนี้ได้อย่างไร
f ไพรม์ของ x จะเท่ากับ ลองดู
เราจะต้องใช้ชุด
กฎผลคูณหรือกฎลูกโซ่
มันจะเท่ากับอนุพันธ์เทียบกับ x ของ x
มันจะเท่ากับตัวนั้น
คูณ e กำลังลบ 2x กำลังสองบวกอนุพันธ์
เทียบกับ x ของ e กำลังลบ 2x กำลังสอง
คูณ x นี่ก็แค่กฎผลคูณตรงนี้

Czech: 
v nichž je derivace tohoto výrazu podle x
buď rovna 0, nebo není definovaná.
Zamysleme se teď nad tím,
jak spočítáme derivaci této funkce.
f(x) s čárkou bude…
Budeme muset použít pravidlo pro
derivaci součinu a také složené funkce.
Bude to derivace podle ‚x‘ z ‚x‘
vynásobená e na (−2 krát (x na druhou))
plus derivace podle ‚x‘ z
e na (−2 krát (x na druhou)),
kterou ještě musíme
vynásobit číslem ‚x‘.
To je jen
pravidlo pro derivaci součinu.

Bulgarian: 
всички места, където 
производната на този израз
спрямо х, или е равна на 0, 
или не е дефинирана.
Нека да помислим за това как можем
 да намерим производната на функцията.
Нека да видим на какво ще бъде равна f', 
т.е. производната на функцията.
Ще трябва да приложим комбинация от
верижното правило и правилото за 
намиране производна на произведение.
Ще получим производната на х
спрямо х, от х,
т.е. ето това,
умножено по е на степен минус 2 
на квадрат плюс производната
спрямо х, от е на степен –2x^2.
От е на степен –2x^2,
умножено по х.
Дотук използвахме само правилото за
 намиране производна на произведение.

English: 
out all the places where
the derivative of this with
respect to x is either equal
to zero or it is undefined.
Let's think about how we can
find the derivative of this.
f prime of x is going
to be, well let's see.
We're going to have to
apply some combination
of the product rule and the chain rule.
It's going to be the derivative
with respect to x of x,
so it's going to be that,
times e to the negative two
x squared plus the derivative
with respect to x of e to
the negative two x squared
times x. This is just the
product rule right over here.

Portuguese: 
onde a derivada disso com 
respeito a x será zero ou indefinido.
Pensemos em como podemos 
encontrar a derivada disso.
Vejamos, f'(x) será -- bom, vejamos, teremos que aplicar 
alguma combinação da regra do produto e da regra da cadeia.
Isso será a derivada com respeito
a x de x vezes exp(-2x^2) mais
a derivada com respeito a 
x de exp(-2x^2) vezes x.
Isso é somente a regra do produto,

Korean: 
x에 관한 미분계수가
0이거나 정의되지 않은
모든 점을 찾고자 합니다
어떻게 이 함수의 미분계수를
구할지 생각해 봅시다
f'(x)를 구하기 위해서
곱의 법칙과 연쇄 법칙을
적용해야 합니다
 
x에 관한 x의 미분계수와
 
e^-2x²의 곱과
x에 관한 e^-2x²의 미분계수와
x의 곱의 합이 됩니다

Czech: 
Derivace x vynásobená
e na (−2 krát (x na druhou))
plus derivace z
e na (−2 krát (x na druhou))
vynásobená číslem ‚x‘.
Kolik to bude?
To, co teď zvýrazňuji fialově,
tedy derivace ‚x‘ podle ‚x‘, se rovná 1.
Tato první část tak bude rovna
e na (−2 krát (x na druhou)).
Dále tu máme derivaci z
e na (−2 krát (x na druhou)).
Udělám to růžově.
Tato část
bude rovna…
Použijeme vzorec
pro derivaci složené funkce.
Derivace z e na (−2 krát (x na druhou))
podle (−2 krát (x na druhou)),
to bude jednoduše
e na (−2 krát (x na druhou)).
Tohle vynásobíme derivací z
(−2 krát (x na druhou)) podle x,
což se rovná
−4 krát x,
takže tady bude
krát −4 krát x.
Samozřejmě tu máme
ještě tohle x.

Portuguese: 
a derivada de x vezes exp(-2x^2) 
mais a derivada de exp(-2x^2) vezes x.
No que resultará isso?
Bom, tudo isso aqui em rosa -- a derivada de x 
com respeito a x -- será somente igual a 1.
Essa primeira parte será igual a exp(-2x^2), e agora a derivada aqui --
-- essa parte aqui será igual a --
bom, apliquemos somente a regra da cadeia.
Derivada de exp(-2x^2) com respeito 
a -2x^2 será somente exp(-2x^2),
e iremos multiplicar aquilo pela 
derivada de -2x^2 com respeito a x.
Isso será então -4x.
Vezes -4x. E, é claro, temos esse x aqui.

Bulgarian: 
Производна от х по 
е на степен –2x^2,
плюс производна от 
е на степен –2x^2 по х.
На какво ще бъде равен 
този израз?
Целият този израз в пурпурно,
т.е. производната на х спрямо х,
просто ще бъде равен на 1.
Тази първа част ще бъде равна на
е на степен –2x^2.
Сега имаме производната на 
е на степен –2x^2.
Ще го запиша в розово.
Тази част ето тук 
ще бъде равна на...
Е, тук просто ще приложим 
верижното правило.
Производна на е на степен –2x^2
спрямо –2x^2,
ще бъде равна просто на 
е на степен –2x^2.
Ще умножим това по
производната на –2x^2 спрямо х.
Това ще бъде равно на –4х.
Тоест по –4х,
и разбира се, имаме този х ето тук.

Korean: 
다음과 같은 함수의 미분계수는
 
아래와 같습니다
이 식은 무엇과 같을까요?
자홍색으로 된 부분은
x에 관한 x의 미분계수인데요
이는 1입니다
식의 앞부분은
e^(-2x²)과 같습니다
그리고 e^(-2x²)의 미분계수는
 
핑크색으로 해보겠습니다
이 부분은
연쇄법칙을 적용하겠습니다
e^(-2x²)의
-2x²에 관한 미분계수는
변함없이 e^(-2x²)입니다
 
x에 관한 -2x²의 미분계수를 곱합니다
-4x가 되겠죠
이를 곱해주고
당연히 x도 곱해줍니다

Thai: 
อนุพันธ์ของ x คูณ e กำลัง
ลบ 2x กำลังสองบวกอนุพันธ์ของ e กำลัง
ลบ 2x กำลังสองคูณ x ตรงนี้
อันนี้จะเท่ากับอะไร?
ทั้งหมดนี้คือสีบานเย็น
อนุพันธ์ของ x เทียบกับ x
มันจะเท่ากับ 1
ส่วนนี่ตรงนี้จะเท่ากับ
e กำลังลบ 2x กำลังสอง
ทีนี้ อนุพันธ์ของ e กำลัง
ลบ 2x กำลังสองตรงนี้
ผมจะทำด้วยสีชมพูนี้นะ
ส่วนนี่ตรงนี้ มันจะเท่ากับ --
เราแค่ใช้กฎลูกโซ่
อนุพันธ์ของ e กำลังลบ 2x กำลังสอง
เทียบกับลบ 2x กำลังสอง นั่น
จะเท่ากับ e กำลังลบ 2x กำลังสอง
เราจะคูณมันด้วย
อนุพันธ์ของลบ 2x กำลังสองเทียบกับ x
มันจะเท่ากับอะไร ลบ 4x
คูณลบ 4x และ
แน่นอน เรามี x นี่ตรงนี้

English: 
Derivative of the x times e to the
negative of two x squared plus
the derivative of e to the
negative two x squared
times x, right over here.
What is this going to be?
Well all of this stuff in magenta,
the derivative of x with respect to x,
that's just going to be equal to one.
This first part is going to be equal
to e to the negative two x squared.
Now the derivative of e to the
negative two x squared over here.
I'll do this in this pink color.
This part right over here,
that is going to be equal to-
We'll just apply the chain rule.
Derivative of e to the
negative two x squared with
respect to negative two
x squared, well that's
just going to be e to the
negative two x squared.
We're going to multiply that times the
derivative of negative two
x squared with respect to x.
That's going to be what, negative four x.
Times negative four x, and of
course we have this x over here.

Portuguese: 
Temos aquele x, vejamos, 
podemos simplificar tudo isso?
Obviamente, ambos esses termos 
tem um exp(-2x^2) --
eu tentarei descobrir se isso 
é indefinido ou igual a zero.
Pensemos um pouco sobre isso.
Vejamos, se isolarmos exp(-2x^2), teremos --
isso é igual a exp(-2x^2) vezes -- 
temos aqui 1 menos 4x^2.
Então essa é a derivada de f. Agora, aonde 
isso será indefinido ou igual a zero?

Czech: 
Bude tu ještě x.
Můžeme to 
nějak zjednodušit?
Oba členy obsahují
e na (−2 krát (x na druhou)).
Musíme nějak přijít na to,
kde je tohle nedefinováno, nebo rovno 0.
Trochu se nad
tím tedy zamysleme.
Když vytkneme
e na (−2 krát (x na druhou))...
Napíšu to zeleně.
...tak nám vyjde, že toto se rovná
e na (−2 krát (x na druhou)) krát...
Musíme to vynásobit výrazem
(1 minus 4 krát (x na druhou)).
Toto je tedy
derivace funkce f(x).
Kdy tohle bude nedefinováno,
nebo rovno 0?

Bulgarian: 
Имаме този х ето тук. Нека да видим,
дали може да опростим този израз?
Очевидно тези два члена съдържат 
е на степен –2x^2.
Ще се опитам да намеря
 къде този израз
не е дефиниран, 
или къде е равен на 0.
Нека да помислим 
върху това за малко.
Ако изнесем пред скоби
 е на степен –2x^2...
ще го направя в зелено.
Ще получим, че това е равно на 
е на степен –2x^2 по
1 – 4х^2.
1 минус 4 по х на квадрат.
Това е производната на функцията f.
Къде този израз няма да бъде 
дефиниран или ще бъде равен на 0.
е на степен –2x^2

English: 
We have that x over there and let's see,
can we simplify it at all?
Well obviously both of these terms have
an e to the negative two x squared.
I'm going to try to
figure out where this is
either undefined or where
this is equal to zero.
Let's think about this a little bit.
If we factor out e to the
negative two x squared,
I'll do that in green.
We're going to have,
this is equal to e to the
negative two x squared times,
we have here, one minus four x squared.
One minus four x squared.
This is the derivative of f.
Where would this be
undefined or equal to zero?
e to the negative two x squared,

Korean: 
한 번 봅시다
이 식을 단순화시킬 수 있을까요?
이 두 식은 모두 e^(-2x²)을 가집니다
 
이 식이 어떤 점에서
정의되지 않거나 0인지를
찾아보겠습니다
잠깐 생각해 봅시다
e^(-2x²)을 묶어내면
초록색으로 해보죠
 
이는 e^(-2x²)과
1-4x²의 곱과 같습니다
 
아래의 식이 f(x)의 미분계수입니다
어떤 점에서 아래 식이
0이거나 정의되지 않을까요?
 

Thai: 
เรามี x ตรงนั้นแล้วลองดู
เราจัดรูปมันได้ไหม?
แน่นอนทั้งสองเทอมนี้มี
e กำลังลบ 2x กำลังสอง
ผมจะพยายามหาว่าพจน์นี้
ไม่นิยาม หรือมีค่าเป็น 0 ที่ไหน
ลองคิดกันสักหน่อย
ถ้าเราแยก e กำลังลบ 2x กำลังสองออกมา
ผมจะทำด้วยสีเขียวนะ
เราจะได้
อันนี้เท่ากับ e กำลังลบ 2x กำลังสองคูณ
เรามีตรงนี้ 1 ลบ 4x กำลังสอง
1 ลบ 4x กำลังสอง
นี่คืออนุพันธ์ของ f
แล้วอันนี้จะไม่นิยามหรือเท่ากับ 0 ตรงไหน?
e กำลังลบ 2x กำลังสอง

Portuguese: 
Vejamos, exp(-2x^2) será definido para 
qualquer valor de x. Esta parte será definida.
E essa parte também será 
definida para qualquer valor de x.
Então não há pontos onde a função é indefinida. 
Vejamos onde ela será igual a zero.
Temos então esse produto dessas 
duas expressões igual a zero.
exp(-2x^2), que nunca será zero.
Se você tiver um expoente bastante negativo,
você se aproximará de zero, 
mas nunca chegará a zero.
Então essa parte não poderá ser zero, mas se o produto dos 
dois for zero, ao menos um deles tem que ser zero.
Logo, a única maneira de obter f'(x) igual a 0 
é quando 1 - 4x^2 é igual a zero.
1 - 4x^2 = 0. Deixe-me reescrever isso. 
1 - 4x^2 = 0, quando isso acontece?
Nós somente temos que calcular.
Adicione 4x^2 em ambos os lados, 
você obtém 1 = 4x^2.

Bulgarian: 
ще бъде дефиниран 
за всяка стойност на х.
Този израз е дефиниран.
А този израз всъщност ще бъде дефиниран 
отново за всяка стойност на х.
Няма точка, където 
производната не е дефинирана.
Нека да помислим кога 
производната ще бъде равна на 0.
Това означава, че произведението 
на тези два израза ще бъде равно на 0.
е на степен –2x^2 никога 
няма да бъде равно на 0.
Ако степента в този израз
изберем да е огромно
 отрицателно число,
то изразът ще клони към 0, но 
никога няма да достигне до нея.
Следователно тази част не може 
да е равна на 0.
Ако произведението от тези 
два израза е равно на 0, то поне
един от тях следва да е равен на 0. 
Следователно единственият начин
да приравним производната f' 
да бъде равна на 0,
е, когато 1 – 4х^2 е равно на 0.
1 – 4х^2 е равно на 0. 
Нека да го запиша.
1 – 4х^2 е равно на 0.
Кога това е изпълнено?
Просто ще решим това уравнение.
Прибавяме 4x^2 към 
двете страни на уравнението
и получаваме 1 = 4x^2.

English: 
this is going to be
defined for any value of x,
this part is going to be defined,
and this part is also going to
be defined for any value of x.
There's no point where this is undefined.
Let's think about when this
is going to be equal to zero.
The product of these two
expressions equalling zero,
e to the negative two x squared,
that will never be equal to zero.
If you get this exponent to be a really,
I guess you could say
very negative number,
you will approach zero but you
will never get it to be zero.
This part here can't be zero.
If the product of two
things are zero at least
one of them has to be
zero, so the only way
we can get f prime of x
to be equal to zero is
when one minus four x
squared is equal to zero.
One minus four x squared is equal
to zero, let me rewrite that.
One minus four x squared is equal
to zero, when does that happen?
This one we can just solve.
Add four x squared to both sides,
you get one is equal to four x squared.

Korean: 
e^(-2x²)는 모든 x의 값에서 정의됩니다
 
이 부분 또한 모든 x의 값에서
정의됩니다
아래 식이 정의되지 않는 점은
없습니다
아래 식이 0이 될 때를 생각해 볼까요?
두 부분의 곱이 0이 되어야 합니다
e^(-2x²)는
절대 0이 될 수 없습니다
여러분이 만약 이 지수 값을
매우 작은 음수 값으로 만든다면
0에 가까워질 수는 있지만
절대 0이 될 수는 없습니다
이 부분은 0이 될 수 없습니다
두 식의 곱이 0이 되려면 최소한
둘 중 하나는 0이여야 합니다
f'(x)가 0이 되게 하는 유일한 방법은
1-4x²이 0일 때입니다
1-4x²이 0일 때
다시 적어보죠
 
언제 이게 가능할까요?
풀어보겠습니다
양변에 4x²을 곱해줍니다
여러분들은 1=4x²를 얻습니다

Thai: 
อันนี้จะนิยามสำหรับค่า x ใดๆ
ส่วนนี้จึงนิยาม
และส่วนนี้จะนิยามสำหรับค่า x ใดๆ
จึงไม่มีจุดใดที่ฟังก์ชันไม่นิยาม
ลองคิดดูว่าพจน์นี้จะเท่ากับ 0 เมื่อใด
ผลคูณของสองพจน์นี้เท่ากับ 0
e กำลังลบ 2x กำลังสอง
มันจะไม่มีทางเท่ากับ 0
ถ้าคุณได้พจน์ยกกำลังนี้
เป็นจำนวนลบมากๆ
คุณจะเข้าใกล้ 0 แต่คุณไม่มีทางได้ 0 พอดี
ส่วนนี้จึงเป็น 0 ไม่ได้
ถ้าผลคูณของสองตัวนี้เป็น 0 อย่างน้อย
ตัวหนึ่งต้องเป็น 0 แล้ววิธีเดียว
ที่เราได้ f ไพรม์ของ x เท่ากับ 0 คือ
1 ลบ 4x กำลังสองเท่ากับ 0
1 ลบ 4x กำลังสองเท่ากับ
0 ขอผมเขียนมันใหม่นะ
1 ลบ 4x กำลังสองเท่ากับ
0 มันเกิดขึ้นเมื่อไหร่?
อันนี้เราแก้ได้
บวก 4x กำลังสองทั้งสองข้าง
คุณได้ 1 เท่ากับ 4x กำลังสอง

Czech: 
e na (−2 krát (x na druhou)),
to bude definováno pro všechna x.
Tato část bude rovněž
definována pro všechna x,
takže nejsou žádné body,
kde není derivace definovaná.
Zamysleme se tedy nad tím,
kdy bude tohle rovno 0.
Máme součin dvou výrazů,
který se rovná 0.
e na (−2 krát (x na druhou))
se nikdy nebude rovnat 0.
Pokud by byl tento exponent
velmi záporné číslo,
vyjde nám hodnota blížící se nule,
ale nikdy to nebude přesně 0.
Tato část tudíž
nemůže být rovna 0.
Aby byl ale součin roven 0,
alespoň jeden činitel musí být roven 0.
Jediná možnost, jak může
být derivace f(x) rovna nule,
je ta, že (1 minus 4 krát (x na druhou))
se bude rovnat 0.
(1 minus 4 krát (x na druhou)) se rovná 0,
jen to přepíšu.
(1 minus 4 krát (x na druhou)) se rovná 0,
kdy k tomu dojde?
Tohle snadno vyřešíme, nejprve k oběma
stranám přičteme 4 krát (x na druhou).
Dostaneme, že
1 se rovná 4 krát (x na druhou).

Bulgarian: 
Разделяме двете страни на 4
и получаваме 1/4 е равно на х^2.
За кои стойности на х
това условие е изпълнено?
Коренуваме (намираме квадратен корен)
двете страни на уравнението
и получаваме х е равно на 
плюс или минус 1/2.
Минус 1/2 на квадрат е равно на 1/4.
Плюс 1/2 на квадрат е равно на 1/4.
Ако х е равно на плюс или минус 1/2,
то f', или производната, е равна на 0.
Нека да го запиша по следния начин.
f' от 1/2 е равно на 0,
а ето в този израз 
може да го провериш.
И f' от минус 1/2 е равно на 0.
Ако някой попита къде се намират 
критичните точки за тази функция –
критични точки –
то това са х равно на 1/2 и минус 1/2.

English: 
Divide both sides by four, you get
one fourth is equal to x squared.
Then what x values is this true at?
We just take the plus or minus
square root of both sides
and you get x is equal to
plus or minus one half.
Negative one half squared is one fourth,
positive one half squared is one fourth.
If x equals plus or
minus one half f prime,
or the derivative, is equal to zero.
Let me write it this way.
f prime of one half is equal to zero,
and you can verify that right over here.
And f prime of negative
one half is equal to zero.
If someone asks what are
the critical numbers here,
they are one half and negative one half.

Czech: 
Obě strany nyní
vydělíme 4,
čímž dostaneme, že
(1 lomeno 4) se rovná x na druhou.
Pro která x
tohle platí?
Obě strany odmocníme a na jednu
stranu přidáme plus minus,
čímž dostaneme, že
x se rovná plus nebo minus (1 lomeno 2).
(−1 lomeno 2) na druhou je 1 lomeno 4
a (1 lomeno 2) na druhou je 1 lomeno 4.
Když je tedy x rovno
plus nebo minus (1 lomeno 2),
f s čárkou, tedy derivace,
se rovná 0.
Napíšu to takto.
f s čárkou v bodě (1 lomeno 2)
se rovná 0.
Můžete si to
tady ověřit.
f s čárkou v bodě
minus (1 lomeno 2) se rovná 0.
Takže když se nás někdo zeptá
na stacionární body téhle funkce,
tak jde o body (1 lomeno 2)
a minus (1 lomeno 2).

Portuguese: 
Divida ambos os lados por 4 e você obtém 1/4 = x^2, 
e então quais serão os valores de x?
Bom, calculemos mais ou menos a raiz quadrada em 
ambos os lados e você obtém x = ±1/2.
(-1/2)^2 é igual a 1/4, (+1/2)^2 será 1/4. Logo, x = ±1/2.
f'(x) ou a derivada será igual a zero. Vou escrever desta forma.
f'(1/2) = 0, e você poderá verificar 
isso logo aqui, e f'(-1/2) = 0.
Então, se alguém perguntasse: "Qual são os pontos 
críticos aqui?" Eles serão 1/2 e -1/2.
Legendado por Musa Morena Marcusso Manhães

Korean: 
양변을 4로 나눠줍니다
여러분은 1/4 = x²을 얻습니다
x가 얼마여야 할까요?
양변에 ±√ 를 취해주면
여러분은 x=±1/2를 얻게 됩니다
-1/2의 제곱은 1/4이고
+1/2의 제곱은 1/4입니다
x가 ±1/2이면 f'(x)는
0이 됩니다
이렇게 적어보죠
f'(1/2)=0
여기서 확인할 수 있죠
그리고 f'(-1/2)=0
이 식의 극점이 무엇인지 묻는다면
1/2와 -1/2가 됩니다

Thai: 
หารทั้งสองข้างด้วย 4 คุณจะได้
1/4 เท่ากับ x กำลังสอง
แล้วค่า x ใดทำให้อันนี้เป็นจริง?
เราแค่หาบวกหรือลบรากที่สองทั้งสองข้าง
แล้วคุณได้ x เท่ากับบวกหรือลบ 1/2
ลบ 1/2 กำลังสองได้ 1/4
บวก 1/2 กำลังสองได้ 1/4
ถ้า x เท่ากับบวกหรือลบ 1/2, f ไพรม์
หรืออนุพันธ์จะเท่ากับ 0
ขอผมเขียนมันแบบนี้นะ
f ไพรม์ของ 1/2 เท่ากับ 0
และคุณทดสอบได้ตรงนี้
และ f ไพรม์ของลบ 1/2 เท่ากับ 0
ถ้ามีคนถามว่าจำนวนวิกฤตตรงนี้คืออะไรบ้าง
พวกมันได้แก่ 1/2 หรือลบ 1/2
