
Czech: 
Řekněme, že máme desku kartonu
o rozměrech 20 krát 30 palců.
Pokusím se ji
co nejlépe nakreslit.
Mohla by 
vypadat nějak takto.
Toto je moje
kartonová deska.
Abychom nezapomněli její rozměry,
tak sem napíšu 20 a 30 palců.
Nyní odřežeme
rohy této desky.
Všechny odříznuté
rohy budou čtverce.
Z každého rohu odřízneme
čtverec o straně x.
Jakmile tyto rohy uřežeme,
můžeme přeložit přečnívající části.
Nakreslím je.
Představte si, že to přeložíme
zde, zde a zde,
čímž vytvoříme
krabici.

Portuguese: 
Digamos que temos um pedaço de papelão
de 20 polegadas por 30 polegadas.
Deixe-me desenhar o papelão
da melhor forma.
Pode ser algo assim.
Isso é o meu pedaço de papelão.
E só para reforçar,
temos 20 polegadas por 30 polegadas.
O que faremos é cortas as bordas.
Todas as bordas serão quadrados,
e iremos cortar bordas de dimensões
x por x de cada borda deste papelão.
Após cortar as bordas,
iremos dobrar as laterais.
Deixe-me desenhá-las.
Você pode ver que poderíamos dobrar aqui,
e aqui e formar uma caixa.

English: 
Let's say that we have
a sheet of cardboard
that is 20 inches by 30 inches.
Let me draw the cardboard
as neatly as I can.
So it might look
something like that.
So that is my
sheet of cardboard.
And just to make sure
we know the dimensions,
there's 20 inches by 30 inches.
And what we're
going to do is cut
out the corners
of this cardboard.
And all the corners are
going to be squares,
and we're going to cut
out an x by x corner
from each of the corners of this
piece of cardboard-- x by x.
Over here, x by x, and
then over here, x by x.
And what we'll do is after
we cut out those corners,
we can essentially
fold down the flaps.
Let me draw the flap.
So you could imagine we
can fold right there,
we could fold right there,
we could fold right there,
and we would form a box.

Korean: 
 
가로 30인치 세로 20인치인 
골판지 한 장이 있습니다
가로 30인치 세로 20인치인 
골판지 한 장이 있습니다
직접 그려보겠습니다
직접 그려보겠습니다
직접 그려보겠습니다
직접 그려보겠습니다
직접 그려보겠습니다
직접 그려보겠습니다
직접 그려보겠습니다
사각형의 모서리 부분을
x * x 만큼 잘라냅니다
x * x 만큼 잘라냅니다
 
모서리를 자른 후
점선을 따라 접어올립니다
지금 그리는 점선을 따라 접습니다
 
 
 

Thai: 
 
สมมุติว่าเรามีแผ่นกระดาษกล่อง
ขนาด 20 นิ้วคูณ 30 นิ้ว
ขอผมวาดกระดาษกล่อง
ให้สวยที่สุดเท่าที่จะทำได้
มันอาจเป็นแบบนั้น
นั่นคือแผ่นกระดาษกล่องของผม
เพื่อให้แน่ใจว่าเรารู้ขนาด
มันคือ 20 นิ้วคูณ 30 นิ้ว
และสิ่งที่เราจะทำคือตัด
มุมแผ่นกระดาษกล่องนี้ออก
และมุมทุกมุมจะเป็นรูปสี่เหลี่ยมจัตุรัส
และเราจะตัดมุม x คูณ x
ออกจากมุมของกระดาษนี้แต่ละมุม -- x คูณ x
ตรงนี้ x คูณ x แล้วตรงนี้ x คูณ x
และสิ่งที่เราจะทำคือ 
หลังจากเราตัดมุมเหล่านั้น
เราจะพับปีกลงได้
ขอผมวาดปีกนะ
คุณคงนึกออก เราพับตรงนี้ได้
เราพับตรงนี้ได้ เราพับตรงนี้ได้
และเราตั้งกล่องขึ้นมาได้

Bulgarian: 
Нека да кажем, че разполагаме 
с парче картон,
който е 20 инча на 30 инча.
Нека да нарисувам картон, 
доколкото мога.
Може да изглежда като нещо такова.
Това е моето парче картон.
И само за да се уверя,
 че знаем размерите,
тази страна е 20 инча, а тази е 30 инча.
Това, което ще направим, е 
да изрежем ъглите на този картон.
И всички ъгли ще бъдат изрязани 
под формата на квадрат.
Ще изрежем х на х квадрат
от всеки от ъглите на това парче картон.
Ето тук, х на х, а след това 
ето тук х на х.
И това, което ще направим 
след като изрежем ъглите,
е да сгънем надолу страните.
Нека да означа страните.
Може да си представиш, че 
сгъваме ето тук.
Може да сгънем ето тук, и ето тук.
И ще оформим кутия.

English: 
I guess you could imagine a
box without a bottom to it,
or you can view a box
without a top to it.
So if we were to
fold everything up,
we would get a container that
looks something like this.
Let me make my best
attempt to draw it.
So it would look like this.
This is one flap folded up.
You can imagine this
flap right over here,
if I were to fold
it up like that,
it now would look like this.
It would now look like this.
The height of the flap is x.
So this distance
right over here is x.
And then if I were to fold
this flap, if I were-- let
me do that a little bit neater.
If I were to fold this
flap right over here,
if I were to fold that up,
then it would look like this.
Let me make my best
attempt to draw it.
It would look like that.

Thai: 
ผมว่า คุณคงนึกภาพกล่องที่ไม่มีก้นได้
หรือคุณมองเป็นกล่องที่ไม่มีฝาก็ได้
ถ้าเราพับทุกด้านขึ้นมา
เราจะได้ภาชนะที่เป็นแบบนี้
ขอผมวาดให้ดีที่สุดนะ
มันจะเป็นแบบนี้
 
อันนี้คือปีกด้านหนึ่งพับขึ้น
คุณคงนึกภาพปีกนี่ตรงนี้ได้
ถ้าผมพับมันขึ้นแบบนั้น
ตอนนี้ มันจะเป็นแบบนี้
ตอนนี้มันจะเป็นแบบนี้
ความสูงของปีกคือ x
ระยะนี่ตรงนี้ก็คือ x
แล้วถ้าผมพับปีกนี้ ถ้าผม -- ขอ
ผมวาดให้สวยหน่อย
ถ้าผมพับปีกนี่ตรงนี้
ถ้าผมพับปีกนั้นขึ้น มันจะเป็นแบบนี้
 
ขอผมพยายามวาดให้ดีที่สุดนะ
มันจะเป็นแบบนั้น

Czech: 
V podstatě krabici bez dna,
nebo krabici bez víka.
Jakmile všechno přeložíme,
dostaneme takovouto krabici.
Zkusím to nakreslit
co nejlépe.
Bude to
vypadat takto.
Toto je jedna přeložená
přečnívající část.
Jde o tuto
přečnívající část.
Když ji takto přeložím nahoru,
bude to vypadat nějak takto.
Výška přečnívající
části je x.
Tato vzdálenost
je tedy x.
Když přeložím
tuto část...
Nakreslím to
trochu lépe.
...když přeložím nahoru i tuto část,
bude to vypadat nějak takto.
Snažím se to
nakreslit co nejlépe.
Vypadalo by to
nějak takto.

Korean: 
바닥이 없거나 뚜껑이 없는
상자가 만들어집니다
그럼 그 모습을 입체적으로
그럼 그 모습을 입체적으로
옆 부분에 그리겠습니다
옆 부분에 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
 
이 사각형의 높이는 x 입니다
이 사각형의 높이는 x 입니다
 
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다

Bulgarian: 
Може да си представим, че това 
е кутия без дъно към нея,
или да го разглеждаш като кутия 
без капак към нея.
Ако сгънем всичко нагоре,
то ще получим кутия, която 
изглежда като нещо такова.
Нека да опитам да го начертая 
по най-добрия начин.
Би изглеждало ето така.
 
Това е едната страна, сгъната нагоре.
Може да си представиш 
ето тази страна ето тук,
ако е сгъната нагоре ето така.
Сега ще изглежда по този начин.
Сега би изглеждало по този начин.
Височината на стената е х.
Тоест, това разстояние ето тук 
е равно на х.
Ако след това сгънем тази страна - нека
да я направя малко по-добре.
Ако исках да сгъна тази страна ето тук,
ако исках да я прегъна нагоре, 
то би изглеждала ето така.
 
Нека да направя най-добрия опит 
да я начертая.
Би изглеждала по следния начин.

Portuguese: 
Você pode imaginar uma caixa sem fundo
ou uma caixa sem tampa.
Se dobrássemos tudo,
teríamos algo assim.
Deixe-me tentar desenhar isso.
Ficaria algo assim.
Esta lateral está dobrada para cima.
Você pode imaginar que se eu dobrasse
esta lateral para cima, ficaria assim.
A altura dessa lateral é x.
Esta distância é x.
E se eu dobrasse -- deixe-me fazer isso
de uma maneira mais organizada.
Seu dobrasse esta lateral aqui,
ficaria desse jeito.
Deixe-me desenhá-la
do melhor jeito possível.
Ficaria assim.

Korean: 
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
입체 도형을 그리겠습니다
 
이제 다 그렸습니다
점선을 따라 접으면
다음과 같은 상자가 나옵니다
상자의 부피를 최대로 
만드는 것이 문제입니다
상자의 부피를 최대로 
만드는 것이 문제입니다
 
x의 값을 조정해 상자의 부피를 
변화할 수 있습니다
상자의 부피를 x에 대한 식으로
나타내어 봅시다
상자의 부피를 x에 대한 식으로
나타내어 봅시다
그 전에
상자의 높이, 너비를 x에 관한 
식으로 표현합시다
처음 잘라낸 사각형의 한 변의 길이는
자른 후 접어 올려 만든 상자의
높이와 같기 때문에

English: 
And then I would fold
that back flap up.
So the back flap would
look something like that.
That would be the back flap.
It would look
something like that.
And then this flap
over here would--
if I fold it up would
look something like that.
And then of course, my
base of my whole thing,
so this whole region right over
here of my piece of cardboard,
would be the floor of this
box that I'm constructing.
And what I want to do
is I want to maximize
the volume of this box.
I want to maximize
how much it can hold.
And I want to maximize it by
picking my x appropriately.
So let's think about what
the volume of this box
is as a function of x.
Well, in order to
do that, we have
to figure out all the dimensions
of this box as a function of x.
We already know that this
corner right over here,
which is made up of when
this side and this side
connect when you fold
these two flaps up,

Portuguese: 
E eu dobraria essa lateral
para cima e ficaria assim.
Isso seria a lateral traseira.
Parecida com algo assim.
E esta lateral aqui --
se eu a dobrasse, ficaria assim.
E tenho também a base de tudo isso.
Toda esta região do meu pedaço de papelão
seria o chão da caixa que estou montando.
O que eu quero
é maximizar o volume da caixa.
Quero maximizar o quanto
esta caixa pode conter.
E quero maximizar o volume
escolhendo um x adequado.
Vamos pensar sobre o volume
desta caixa em função de x.
Para fazer isso, devemos descobrir todas
as dimensões da caixa em função de x.

Thai: 
แล้วผมจะพับปีกหลังขึ้น
ปีกหลังจะเป็นแบบนั้น
นั่นคือปีกหลัง
มันจะเป็นแบบนั้น
แล้วปีกนี่ตรงนี้จะ --
ถ้าผมพับันขึ้น จะได้แบบนั้น
แล้วแน่นอน ฐานของผม ทั้งหมดนี้
พื้นที่ทั้งหมดนี่ตรงนี้ของกระดาษกล่อง
จะเป็นพื้นของกล่องนี้ที่ผมกำลังสร้างอยู่
และสิ่งที่ผมอยากทำคือ ผมอยากให้
ปริมาตรกล่องนี้มากที่สุด
ผมอยากให้ปริมาณที่มันจุได้มีค่าสูงสุด
และผมอยากให้มันมีค่าสูงสุด 
โดยเลือก x อย่างเหมาะสม
ลองคิดว่าปริมาตรของกล่องนี้คืออะไร
เป็นฟังก์ชันของ x
เวลาทำ เราต้อง
หาขนาดทั้งหมดของกล่องนี้เป็นฟังก์ชันของ x
เรารู้แล้วว่ามุมนี่ตรงนี้
ซึ่งประกอบเป็นด้านนี้และด้านนี้
เชื่อมกันเวลาคุณพบปีกสองด้านนี้ขึ้น

Bulgarian: 
След това ще сгъна нагоре 
ето тази страна.
Тогава задната стена ще изглежда 
като нещо такова.
Това ще бъде задната стена.
Би изглеждало по следния начин.
Тогава тази стена ето тук –
ако я сгъна ето така – ще изглежда 
по следния начин.
Накрая, разбира се, това е 
основата на цялото това нещо.
Цялото това пространство ето тук 
от моето парче картон,
ще бъде дъното на тази кутия, 
която конструирам.
И това, което искам да направя, 
е да намеря максималния
обем на тази кутия.
Искам да разбера колко възможно 
най-много може да побере.
И искам да намеря максималния обем,
 като избера подходящо х.
Нека да помислим: на какво 
е равен обемът на кутията,
ако е изразен като функция на х.
За да направим това, трябва
да намерим всички обеми на тази 
кутия като функция на х.
Вече знаем, че този ръб ето тук –
който е направен, когато 
тази и тази страна
се свържат, т.е. се прегънат 
тези две страни нагоре –

Czech: 
Potom bych nahoru
přeložil tuto zadní část.
Zadní část by tedy
vypadala nějak takto.
To by byla
zadní část.
Bude vypadat
nějak takhle.
A když nahoru přeložím tuto část,
bude to vypadat nějak takto.
Samozřejmě tu mám
i podstavu celé krabice.
Celá tato část bude dnem krabice,
kterou se snažím vyrobit.
A tuhle krabici chci vyrobit tak,
aby měla co největší možný objem.
Chci maximalizovat to,
kolik se toho do ní vejde,
a chci toho dosáhnout tak,
že vhodně zvolím x.
Zamysleme se, čemu se objem krabice
rovná jakožto funkce proměnné x.
Abychom to zvládli, musíme všechny rozměry
krabice vyjádřit jako funkci proměnné x.
Už víme, že tento roh,
který vznikne složením těchto dvou částí,

Bulgarian: 
ще бъде равен на същата 
височина като този.
Същата височина има и този ръб.
Височината на кутията ще бъде 
равна на х.
А на какво е равна широчината?
На какво е равна широчината 
на тази кутия?
Широчината на кутията ще бъде
равна на това разстояние ето тук.
А това разстояние ще бъде 20 инча, 
но не минус х, а минус 2х.
Следователно широчината на кутията
 ще бъде равна на 20 – 2х.
Ето тук се вижда.
Цялото това разстояние е равно на 20.
Изваждаш този х, изваждаш този х,
и получаваш разстоянието ето тук.
Следователно то е равно на 20 – 2х.
А сега, по същата логика, на какво 
е равна дължината на кутията?
На какво е равно ето това 
разстояние ето тук?
Това разстояние е всъщност 
това разстояние ето тук.
Знаем, че цялото това разстояние
 е равно на 30 инча.
Ако извадим този х и извадим 
и този х от него,
то получаваме разстоянието, 
което ни интересува.

Czech: 
bude mít stejnou výšku
jako všechny ostatní rohy.
Výška této
krabice bude x.
Ale jaká
bude šířka?
Jaká bude šířka
této krabice?
Šířka krabice bude
tato vzdálenost.
Tato vzdálenost bude
20 palců minus 2 krát x.
Toto tedy bude
20 minus 2 krát x.
Vidíte to zde.
Tato celá
vzdálenost je 20,
od ní odečteme
jedno x i druhé x,
čímž dostaneme
tuto vzdálenost.
Je to tedy
20 minus 2 krát x.
Když nyní použijeme stejnou logiku,
čemu se rovná hloubka krabice?
Jaká je tato
vzdálenost?
To odpovídá
této vzdálenosti.
Víme, že tato celá
vzdálenost je 30 palců.
Když odečteme toto x a také tohle x,
dostaneme vzdálenost, kterou hledáme.

Portuguese: 
Já sabemos que este canto, que resulta
de dobrar este lados, terá esta altura.
A altura desta caixa será x.
Mas e a largura?
Qual será a largura desta caixa?
A largura da caixa será esta distância.
E esta distância será 20
polegadas menos dois x.
Toda esta distância é 20.
Você subtrai este x, esse x
e obtém esta distância.
É 20 menos dois x.
E qual é a profundidade da caixa?
Quanto é essa distância?
É igual a esta distância de 30 polegadas.
Se subtrairmos dois x da distância,
vamos obter a distância que queremos.

Korean: 
상자의 높이는 x입니다
 
 
그럼 상자의 세로는 얼마입니까?
 
상자의 세로는
이 부분의 길이와 같습니다
저 길이는 20 - 2x 가 됩니다
저 길이는 20 - 2x 가 됩니다
저 길이는 20 - 2x 가 됩니다
 
이 전체가 20 이고
2개의 x를 빼면 됩니다
 
따라서 20 - 2x 가 됩니다
그럼 상자의 가로는 얼마일까요?
 
 
저 전체 길이는 30 이고
2개의 x를 빼주면
2개의 x를 빼주면

English: 
that's going to be the
same height over there.
That's going to be the
same height over there.
The height of this
box is going to be x.
But what's the width?
What is the width of
this box going to be?
Well, the width of
the box is going
to be this distance
right over here.
And this distance is going
to be 20 inches minus not 1x,
but minus 2 x's.
So this is going
to be 20 minus 2x.
You see it right over here.
This whole distance is 20.
You subtract this x,
you subtract this x,
and you get this
distance right over here.
So it's 20 minus 2x.
Now, the same logic, what
is the depth of the box?
What is that distance
right over there?
Well, that distance is this
distance right over here.
We know that this entire
distance is 30 inches.
If we subtract out this x
and we subtract out this x,
we get the distance
that we care about.

Thai: 
มันจะมีความสูงเท่ากันตรงนี้
มันจะสูงเท่ากันตรงนี้
ความสูงของกล่องนี้จะเท่ากับ x
แต่ความกว้างเป็นเท่าใด?
ความกว้างของกล่องนี้จะเป็นเท่าใด?
ความกว้างของกล่องจะ
เป็นระยะนี่ตรงนี้
และระยะนีจะเท่ากับ 20 นิ้วลบ ไม่ใช่ 1x
แต่ลบ 2x
มันจะเท่ากับ 20 ลบ 2x
คุณเห็นมันตรงนี้
ระยะทั้งหมดนี้คือ 20
คุณลบ x นี้ คุณลบ x นี้
แล้วคุณได้ระยะนี่ตรงนี้
มันก็คือ 20 ลบ 2x
ทีนี้ ด้วยเหตุผลเดียวกัน 
ความลึกของกล่องเป็นเท่าใด?
ระยะนั่นตรงนั้นเป็นเท่าใด?
ระยะนั้นคือระยะนี่ตรงนี้
เรารู้ว่าระยะทั้งหมดนี้คือ 30 นิ้ว
ถ้าเราลบ x นี้แล้วเราลบ x นี้
เราจะได้ระยะที่เราสนใจ

English: 
So this is going
to be 30 minus 2x.
So now we have all
of the dimensions.
So what would the volume
be as a function of x?
Well, the volume
as a function of x
is going to be equal
to the height, which
is x, times the width, which
is 20 minus x-- sorry, 20
minus 2x times the depth,
which is 30 minus 2x.
Now, what are possible values of
x that give us a valid volume?
Well, x can't be less than 0.
You can't make a
negative cut here.
Somehow we would have to add
cardboard or something there.
So we know that x is going to
be greater than or equal to 0.
So let me write this down.
x is going to be greater
than or equal to 0.
And what does it
have to be less than?
Well, I can cut at
most-- we can see here

Thai: 
อันนี้จะเท่ากับ 30 ลบ 2x
ทีนี้ เรามีขนาดทั้งหมดแล้ว
ปริมาตรจะเป็นเท่าใดเป็นฟังก์ชันของ x?
ปริมาตร เป็นฟังก์ชันของ x
จะเท่ากับความสูง ซึ่ง
ก็คือ x คูณความกว้าง ซึ่งก็คือ 20 ลบ x
-- โทษที 20
ลบ 2x คูณความลึก ซึ่งก็คือ 30 ลบ 2x
 
ทีนี้ ค่า x ที่เป็นไปได้ 
ที่ให้ปริมาตรออกมาคืออะไร?
x น้อยกว่า 0 ไม่ได้
คุณตัดให้เป็นลบไม่ได้
ไม่อย่างนั้น เราต้องต่อกระดาษ
หรืออะไรประมาณนั้น
เราจึงรู้ว่า x จะมากกว่าเท่ากับ 0
ขอผมเขียนอันนี้ลงไปนะ
x จะะมากกว่าเท่ากับ 0
และมันต้องน้อยกว่าอะไร?
ผมตัดได้อย่างมาก -- เราเห็นตรงนี้ได้

Korean: 
30 - 2x를 구할 수 있습니다
이제 필요한 값들을 다 구했습니다
그러면 상자의 부피를 x로 나타내봅시다
상자의 부피는
높이 가로 세로를 곱한 값이므로
다음과 같이 표현 가능합니다
다음과 같이 표현 가능합니다
다음과 같이 표현 가능합니다
이제 x의 범위를 구해봅시다
우선 x는 음수가 될 수 없습니다
 
 
따라서 x는 0 이상입니다
 
 
그럼 최댓값은 얼마일까요?
분홍색 부분이 0이 되지 않도록

Portuguese: 
Então esta distância será 30 menos dois x.
Agora temos todas as dimensões.
Qual seria o volume em função de x?
O volume como uma função de x
seria igual à altura, que é x,
vezes a largura, que é 20 menos dois x,
vezes a profundidade,
que é 30 menos dois x.
Quais são os possíveis valores de x
que nos dão um volume válido?
x não pode ser menor que zero.
Não podemos fazer um corte negativo.
De alguma forma, temos que adicionar
papelão ou alguma coisa aqui.
Sabemos que x será maior ou igual a zero.
-- Deixe-me escrever isso. --
x será maior ou igual a zero.
E qual será o maior valor para x?

Czech: 
Tohle tedy bude
30 minus 2 krát x.
Nyní už známe
všechny rozměry,
takže jak vyjádříme objem
jako funkci proměnné x?
Objem vyjádřený jako
funkce x se rovná výška, což je x,
krát šířka, která je
20 minus x...
Pardon, 20 minus 2 krát x.
...krát hloubka,
a ta je 30 minus 2 krát x.
Pro které hodnoty x
dostaneme smysluplný objem?
x nemůže být
menší než 0.
Nemůžeme uříznout
zápornou délku.
To by znamenalo nějak
přidat další kus kartonu.
Víme tedy, že x musí být
větší nebo rovno 0.
Napíšu si to.
x je větší
nebo rovno 0.
Zároveň ale musí být
menší než co?
Nejvíce mohu odříznout…

Bulgarian: 
Това ще бъде равно на 30 – 2х.
Сега имаме всички размери.
Как ще изглежда обемът 
като функция на х?
Обемът, като функция на х,
ще бъде равен на височината, която
е равна х, умножено по широчината, 
която е равна на 20 –х. Извинявам се!
20 – 2х, умножено по дължината, 
която е равна на 30 – 2х.
А сега, какви са възможните стойности 
за х, за които се получава реален обем?
х не може да бъде по-малко от 0.
Не може да изрежеш отрицателен 
размер от картона.
Все пак трябва да добавим картон 
или нещо друго там.
Знаем, че х ще бъде число, 
по-голямо или равно на 0.
Нека да го запиша.
х ще бъде по-голямо или 
равно на 0.
А от какво трябва да бъде по-малко?
Мога най-много да изрежа...
Може да видим ето тук,

Czech: 
Vidíme, že tato růžová
délka je 20 minus 2 krát x.
Toto musí být
také větší než 0.
Bude to vždy menší
než 30 minus 2 krát x,
ale 20 minus 2 krát x
musí být větší nebo rovno 0.
Nemůžeme uřezat více kartonu,
než kolik ho máme.
Jinými slovy 20 musí být
větší nebo rovno 2 krát x,
tedy 10 musí být
větší nebo rovno x,
což je jinými slovy řečeno,
že x musí být menší nebo rovno 10.
To je jiný
odstín žluté.
x musí být menší
nebo rovno 10.
x tedy musí být
mezi 0 a 10.
Jinak bychom uřízli více, než kolik máme
k dispozici, nebo bychom naopak přidali.
Nejprve se podívejme na objem pro krajní
body našeho de facto definičního oboru,
tedy čísel, kterých x může
nabývat, aby měl objem smysl.
Když je x rovno 0,
čemu se rovná objem?

English: 
the length right over here, this
pink color, this mauve color,
is 20 minus 2x.
So this has got to
be greater than 0.
This is always going to be
shorter than the 30 minus 2x,
but the 20 minus 2x has to be
greater than or equal to 0.
You can't cut more
cardboard than there is.
Or you could say that 20 has to
be greater than or equal to 2x,
or you could say
that 10 is going
to be greater than
or equal to x, which
is another way of saying that
x is going to be less than
or equal to 10.
That's a different
shade of yellow.
x is going to be less
than or equal to 10.
So x has got to be
between 0 and 10.
Otherwise we've cut too
much, or we're somehow
adding cardboard or something.
So first let's think about
the volume at the endpoints
of our-- essentially of
our domain, of what x
can be for our volume.
Well, our volume when x is
equal to 0 is equal to what?

Thai: 
ความยาวนี่ตรงนี้ สีชมพูนี้ สีม่วงอ่อนนี้
คือ 20 ลบ 2x
มันต้องมากกว่า 0
ค่านี้จะสั้นกว่า 30 ลบ 2x เสมอ
แต่ 20 ลบ 2x ต้องมากกว่าเท่ากับ 0
คุณตัดกระดาษมากกว่าที่มีไม่ได้
หรือคุณบอกได้ว่า 20 ต้องมากกว่าเท่ากับ 2x
หรือคุณบอกได้ว่า 10 จะ
มากกว่าเท่ากับ x
ซึ่งก็เหมือนกับบอกว่า x จะน้อยกว่า
เท่ากับ 10
นั่นคือสีเหลืองอีกเฉดหนึ่ง
x จะน้อยกว่าเท่ากับ 10
x ต้องอยู่ระหว่าง 0 กับ 10
ไม่อย่างนั้นเราจะตัดมากเกินไป หรือเรา
จะต้องเพิ่มกระดาษ อะไรพวกนั้น
อย่างแรก ลองคิดถึงปริมาตรที่จุดปลาย
ของ -- โดเมนของเรา ของค่า x
ที่เป็นไปได้สำหรับปริมาตรของเรา
ปริมาตรของเราเมื่อ x เท่ากับ 0 
นั้นเท่ากับอะไร?

Korean: 
즉 20 - 2x가 0이상이 되도록 합니다
즉 20 - 2x가 0이상이 되도록 합니다
 
또 30 - 2x도 0보다 커야합니다
20 - 2x가 0 이상이면 
30 - 2x도 만족하게 됩니다
20 - 2x가 0보다 크다는 것은
2x보다 20이 더 크다는 것을 의미하고
x보다 10이 더 크다는 것을 
알 수 있습니다
x보다 10이 더 크다는 것을 
알 수 있습니다
 
 
 
 
따라서 x는 저 범위를 가지게 됩니다
 
 
범위의 최대, 최소값을 대입했을 때
부피가 얼마가 나오는지 계산해봅시다
부피가 얼마가 나오는지 계산해봅시다
x가 0일 때 부피는 어떻게 될까요?

Portuguese: 
Posso cortar, no máximo,-- vemos
que esta largura é 20 menos dois x --
Isso tem que ser maior
ou igual a zero.
Isto sempre será menor
que 30 menos dois x,
mas 20 menos dois x
tem que ser maior ou igual a zero.
Não pode cortar mais papelão
do que o disponível.
Ou você poderia dizer que 20
deve ser maior ou igual a dois x,
ou que 10 será maior ou igual a x,
que é outra maneira de dizer
que x será menor ou igual a 10.
- É uma tonalidade
diferente de amarelo -
x será menor ou igual a 10,
então deve estar entre zero e 10.
Se não, estaríamos cortando muito
ou adicionando material.
Primeiro, vamos pensar sobre o volume
nas extremidades -- do nosso domínio,
dos valores de x para o nosso volume.
Qual é o valor do nosso volume
quando x é igual a zero?

Bulgarian: 
дължината ето тук, с този розов цвят, 
този бледоморав цвят –
е равна на 20 – 2х.
Тази дължина следва да е 
по-голяма от 0.
Но трябва и да е по-малка 
от 30 – 2х.
Но 20 – 2х следва да бъде 
по-голямо или равно на 0.
Не може да изрежеш повече картон, 
отколкото имаш.
Или може да кажеш, че 20 следва 
да е по-голямо или равно на 2х.
Получава се, че 10 ще бъде
по-голямо или равно на х,
което е друг начин да кажеш,
 че х ще бъде по-малко или равно на 10.
Това е различен нюанс на жълтото.
х ще бъде по-малко или равно на 10.
Следователно х следва 
да се намира между 0 и 10.
В противен случай или сме изрязали 
твърде много,
или сме добавили още картон.
Нека първо да намерим
кои са крайните точки
на дефиниционното множество, 
т.е. за това, което
х може да се получи от обема.
Обемът, когато х е равно на 0, 
на какво е равен?

Korean: 
0이 됩니다
0이 됩니다
높이가 없기 때문에
부피가 0이 되죠
부피가 0이 되죠
x가 10이면 어떻게 될까요?
x가 10이면 분홍색 부분이 0이 됩니다
x가 10이면 분홍색 부분이 0이 됩니다
따라서 이때도 부피는 0이 됩니다
 
 
 
따라서 0과 10 사이에 
최대 부피가 있을 것입니다
따라서 0과 10 사이에 
최대 부피가 있을 것입니다
우선 그래프를 그려봅시다
 
그래프는 계산기를 이용해 그리겠습니다
그래프는 계산기를 이용해 그리겠습니다
 
 
우선 범위를 설정합니다
우선 범위를 설정합니다
x의 최소값은 0이고
 

Thai: 
เรามี 0 คูณทั้งหมดนี้
และมันค่อนข้างชัดเจน
คุณจะไม่มีความสูงตรงนี้
คุณจึงไม่มีปริมาตรใดๆ
ปริมาตรของเราจึงเท่ากับ 0
ปริมาตรของเราเป็นเท่าใดเมื่อ x เท่ากับ 10?
ถ้า x เท่ากับ 10 แล้วความกว้างตรงนี้
ที่ผมวาดด้วยสีชมพูจะเป็น 0
เหมือนเดิม เราจะไม่มีปริมาตรเลย
และเทอมนี่ตรงนี้ ถ้าเราดูมัน
โดยใช้พีชคณิต จะเท่ากับ 0
ทั้งหมดนี้จึงเท่ากับ 0
ดังนั้น สักแห่งระหว่าง x เท่ากับ 0 กับ x เท่ากับ
10 เราควรได้ปริมาตรสูงสุด
และก่อนที่เราจะวิเคราะห์ด้วยแคลคูลัส
ลองทำด้วยกราฟกันก่อน
ผมจะเอาเครื่องคิดเลข TI-85 ออกมา
ขอผมเอา TI-85 ออกมานะ
อย่างแรก ขอผมเลือกช่วงให้เหมาะสม
ก่อนที่ผมจะพยายามวาดกราฟ
ผมจะใส่กราฟฟังก์ชัน
ขอผมตั้งช่วงก่อน
ค่า x ต่ำสุด ขอผมเลือกเป็น 0
เรารู้ว่า x น้อยกว่า 0 ไม่ได้

Bulgarian: 
Получава се 0, умножено по този израз.
Очевидно е.
Няма да има никаква височина ето тук.
Следователно няма да има 
и никакъв обем,
т.е. обемът ще бъде равен на 0.
На какво е равен обемът, 
когато х е равно на 10?
Ако х е равно на 10, то тогава ширината,
която ето тук съм означил с розово,
 ще бъде равна на 0.
И отново няма да има никакъв обем.
Тогава този член ето тук, ако просто
го разглеждаме алгебрично, 
също ще бъде равен на 0.
Следователно целият израз 
ще бъде равен на 0.
Тогава някъде между х = 0
 и х = 10
следва обемът да достига 
максимална стойност.
Преди да решим задачата аналитично,
 чрез математически анализ,
нека го направим графично.
Ще взема моя удобен калкулатор TI-85.
Нека да взема моя удобен калкулатор TI-85.
Нека първо да избера правилно 
дефиниционното множество,
преди да начертая функцията.
Избирам графична функция.
Нека първо да избера 
дефиниционното множество.
Минималната стойност за х, 
нека да избера да е 0.
Знаем, че х не може 
да е по-малко от 0.

English: 
We can have 0 times
all of this stuff.
And it's pretty obvious.
You're not going to
have any height here.
So you're not going
to have any volume,
so our volume would be 0.
What is our volume
when x is equal to 10?
Well, if x equaled 10,
then the width here
that I've drawn in
pink would be 0.
So once again, we
would have no volume.
And this term right over
here, if we just look at
it algebraically would
also be, equal to 0,
so this whole thing
would be equal to 0.
So someplace in between
x equals 0 and x equals
10 we should achieve
our maximum volume.
And before we do it analytically
with a bit of calculus,
let's do it graphically.
So I'll get my handy TI-85 out.
So let me get my TI-85 out.
And so first let me set
my range appropriately
before I attempt to graph it.
So I'll put my graph function.
Let me set my range.
So my minimum x-value,
let me make that 0.
We know that x cannot
be less than 0.

Portuguese: 
Podemos ter zero vezes tudo isso.
E, obviamente, você não vai ter
nenhuma altura.
Você não terá nenhum volume,
então o volume seria zero.
Qual é valor do volume,
quando x é igual a 10?
Se x é igual a 10, a largura seria zero.
Mais uma vez, não teríamos um volume.
E este termo, se olharmos algebricamente,
também seria zero, então tudo seria zero.
Em algum lugar
entre x igual a zero e x igual a 10
devemos ter nosso volume máximo.
Antes de fazer isso
usando um pouco de cálculo,
faremos isso graficamente.
Usarei a minha TI-85.
Primeiro, deixe-me ajustar
a imagem antes de fazer o gráfico.
Vou colocar a minha função.
Deixe-me ajustar a imagem.

Czech: 
Máme 0 krát všechno ostatní,
takže to je jasné.
Nebudeme mít žádnou výšku,
takže nebudeme mít ani žádný objem.
Objem tedy
bude nulový.
A co objem
když je x rovno 10?
Když je x rovno 10, tak je šířka krabice,
kterou jsem nakreslil růžově, nulová,
takže bychom opět
neměli žádný objem.
Algebraicky to zdůvodníme tak, že tento
výraz je roven 0, takže i to celé je 0.
Někde mezi body x rovno 0
a x rovno 10 je tedy bod,
ve kterém dosáhneme
maximálního objemu.
Než to uděláme analyticky
pomocí diferenciálního počtu,
udělejme to graficky.
Využiji k tomu svou
kalkulačku TI-85.
Nejdříve nastavím meze
definičního oboru a oboru hodnot,
ještě než
udělám graf.
Sem zadám
svoji funkci.
Nyní zadám
meze pro x a y.
Nejmenší hodnota x bude 0, protože
víme, že x nemůže být menší než 0.
Největší hodnota x
bude 10.

English: 
My maximum x-value, well,
10 seems pretty good.
My minimum y-value,
this is essentially
going to be my volume.
I'm not going to
have negative volume,
so let me set that equal 0.
And my maximum
y-value, let's see
what would be reasonable here.
I'm just going to
pick some a random x
and see what type
of a volume I get.
So if x were to be 5, it
would be 5 times 20 minus 10,
which is 10.
So that would be--
did I do that right?
Yeah, 20 minus 2
times 5, so that
would be 10, and then times
30 minus 2 times 5, which
would be 20.
So it would be 5
times 10 times 20.
So you'd get a volume
of 1,000 cubic inches.
And I just randomly
picked the number 5.
So let me give my maximum
y-value a little higher
than that just in case to
that isn't the maximum value.
I just randomly picked that.
So let's say yMax is 1,500,
and if for whatever reason
our graph doesn't
fit in there, then
maybe we can make
our yMax even larger.
So I think this is going
to be a decent range.
Now let's actually input
the function itself.

Korean: 
x의 최대값은 10입니다
상자는 음의 부피를 가질 수 없으므로
최소 부피는 0입니다
최소 부피는 0입니다
최소 부피는 0입니다
최대 부피는 어떻게 해야 할까요?
최대 부피는 어떻게 해야 할까요?
x를 임의로 정하고
부피를 계산해봅시다
x가 5일 때 계산을 해보면
 
 
 
 
 
부피는 5 * 10 * 20
1000 in3이 됩니다
5는 임의로 정한 수이기 때문에
최대가 아닐 것을 대비해서
최댓값은 더 크게 설정해야 합니다
임의로 고르겠습니다
최댓값을 1500이라 합시다
그래프가 맞기 않다면
최댓값을 더 크게 설정하면 됩니다
 
이제 함수를 입력합니다

Czech: 
Nejmenší hodnota y,
přičemž y je v podstatě objem...
Určitě nebudu mít záporný objem,
takže to nastavím jako 0.
Největší hodnota y…
Co by bylo rozumné?
Vyberu nějaké náhodné x a uvidíme,
jaký objem dostanu.
Pokud by x bylo 5, objem by byl
5 krát (20 minus 10), což je 5 krát 10.
Bylo by to…
Mám to správně?
Ano, 20 minus (2 krát 5), to je 10,
a pak krát 30 minus (2 krát 5), což je 20.
Bylo by to tedy 5 krát 10 krát 20,
což je objem 1000 kubických palců.
Číslo 5 jsem jen
tak náhodně vybral.
Největší hodnotu y tedy zvolím trochu
vyšší, kdyby nešlo o maximální objem.
Největší hodnotu y zvolím jako 1500
a pokud by to z nějakého důvodu nestačilo,
tak největší hodnotu y
ještě navýším.
Toto by měly
být dobré meze.
Nyní zadejme
funkci samotnou.

Bulgarian: 
За максималната стойност 
10 изглежда добре.
Минимална стойност стойност за у, 
което всъщност
ще бъде равно на обема.
Не може да се получи 
отрицателен обем,
така че нека да избера 
това да е равно на 0.
Максимална стойност за у –
нека да видим,
какво би било подходящо тук.
Просто ще избера някаква произволна стойност за х
и ще видя какъв обем ще се получи.
Ако х е равно на 5, ще се получи 
5 по 20 минус 10,
което равно на 10.
Тогава ще се получи...
Направих ли го правилно?
Да, 20 минус 2 по 5, това
ще бъде равно на 10, и тогава 
умножено по 30 минус 2 по 5, което
ще бъде равно на 20.
Ще се получи 5 по 10, по 20.
Ще се получи обем от 
1000 кубични инча.
Просто произволно избрах числото 5.
Нека да избера максималната стойност
за у да е малко по-висока,
отколкото тази, просто в случай, че това
не е максимална стойност.
Просто избрах тази произволно.
Нека да кажем, че у max (максимална стойност) е 
равно на 1500 и ако поради някаква причина
графиката не се получи,
тогава може да зададем у max да е
дори още по-голяма стойност.
Мисля, че това е добро 
дефиниционно множество.
Нека сега да въведем и самата функция.

Thai: 
ค่า x สูงสุด 10 ดูใช้ได้
ค่า y ต่ำสุด อันนี้
จะเป็นปริมาตรของผม
ผมจะไม่ได้ปริมาตรเป็นลบ
ขอผมตั้งมันเท่ากับ 0
และค่า y สูงสุดของผม ลองดู
ว่าค่าใดเหมาะสมตรงนี้
ผมจะเลือกค่า x สุ่มๆ
แล้วดูว่าผมได้ปริมาตรสักแค่ไหน
ถ้า x เท่ากับ 5 มันจะเท่ากับ 5 คูณ 20 ลบ 10
ซึ่งก็คือ 10
มันจะ -- ผมทำถูกไหม?
ใช่ 20 ลบ 2 คูณ 5
มันคือ 10 แล้วคูณ 30 ลบ 2 คูณ 5 ซึ่ง
จะได้ 20
มันจะเท่ากับ 5 คูณ 10 คูณ 20
คุณจะได้ปริมาตร 1,000 ลูกบาศก์นิ้ว
และผมแค่เลือก 5 มาอย่างสุ่ม
ขอผมตั้งค่า y สุงสุดให้สูงขึ้น
กว่านั้นหน่อย เผื่อว่ามันไม่ใช่ค่าสูงสุด
ผมแค่เลือกค่าหนึ่งมาสุ่มๆ
สมมุติว่า yMax เท่ากับ 1,500 และถ้ากราฟเกิด
ไม่พอดีกับจอ
เราก็เลือกให้ yMax มากกว่านั้นได้
ผมว่า อันนี้เป็นช่วงที่ดีแล้ว
ทีนี้ ลองใส่ตัวฟังก์ชันลงไป

Portuguese: 
O meu valor mínimo de x é zero
e o valor máximo é 10.
O meu valor mínimo de y
será o meu volume.
Não vou obter volumes negativos,
então vou deixar isso igual a zero.
O meu valor máximo de y
- vejamos um valor razoável-
Vou substituir um valor qualquer de x
e ver que tipo de volume obterei.
Se x fosse igual a cinco, teria cinco
vezes 20 menos 10, que é 10.
Isso seria -- será que está certo?
Sim, 20 menos dois vezes cinco,
que é 10 e vezes 30 menos dois
vezes cinco, que é 20.
Seria cinco vezes 10 vezes 20. Obteríamos
um volume de 1000 polegadas cúbicas.
E escolhi o número cinco ao azar.
Vou colocar um valor máximo para y
um pouco maior, caso esse não seja
o valor máximo do volume.
Eu escolhi esse número arbitrariamente.
Digamos que o y máximo é 1500
e caso o nosso gráfico não caiba,
então podemos aumentar o valor
de y máximo. Acho que assim está bom.
Agora vamos colocar a nossa função.

Portuguese: 
O nosso volume é igual a x vezes 20
menos dois x menos dois x
vezes 30 menos dois x.
Acho que agora podemos fazer o gráfico.
Quero selecionar isso aqui
para fazer o gráfico.
E parece que acertamos na imagem.
Isso nos diz que o volume é uma função
de x entre x igual a zero e x igual a 10,
e parece que há um valor máximo por aqui.
O que farei é usar a função TRACE
para aproximar o valor do ponto de máximo.
Deixe-me traçar esta função.
Aqui o meu volume é 1055,5
e posso ir até 1056.
Isto era 1056,20 e isto é 1056,24,
e posso voltar a 1055.

Thai: 
ปริมาตรของเราเท่ากับ x คูณ 20
ลบ 2x, ลบ 2x คูณ 30 ลบ 2x
 
มันดูใช่
ตอนนี้ ผมว่าเราวาดกราฟได้แล้ว
2nd และผมเลือกตัวบนนี้
ผมจะเลือก Graph
มันดูเหมือนว่าเราทำถูกช่วงแล้ว
อันนี้บอกเราว่าปริมาตร เป็นฟังก์ชันของ x
ระหว่าง x เท่ากับ 0
กับ x เท่ากับ 10 และดูเหมือนว่าเราถึงจุดสูงสุด
แถวๆ นี้
สิ่งที่ผมจะทำ คือผมจะ
ใช้ฟังก์ชัน Trace เพื่อหาคร่าวๆ
ว่าจุดสูงสุดคืออะไร
ขอผมลากตามฟังก์ชันนี้นะ
ผมยังขึ้นไปได้สูงขึ้น สูงขึ้น
โอเค
ตรงนี้ ปริมาตรของผมเป็น 1,055.5
แล้วผมถึง 1,056 ได้
ลองดู นี่คือ 1056.24 นี่คือ 1,056.24
แล้วผมกลับไปที่ 1,055
อย่างน้อย จากระดับการขยาย

English: 
So our volume is
equal to x times 20
minus 2x minus 2x
times 30 minus 2x.
And that looks about right.
So now I think we can graph it.
So 2nd, and I want to
select that up there,
so I'll do Graph.
And it looks like we
did get the right range.
So this tells us volume is a
function of x between x is 0
and x is 10, and it does look
like we hit a maximum point
right around there.
So what I'm going
to do is I'm going
to use the Trace function
to figure out roughly
what that maximum point is.
So let me trace this function.
So I can still go
higher, higher.
OK.
So over there my
volume is 1,055.5.
Then I can get to 1,056.
So let's see, this was
1,056.20, this is 1,056.24,
then I go back to 1,055.
So at least based
on the level of zoom

Bulgarian: 
Обемът е равен на х по
20 минус 2х, по 30 минус 2х.
И това изглежда добре.
Мисля, че сега мога 
да направя графиката.
Въвеждам данните и искам 
да избера ето тази опция.
Натискам Graph.
Изглежда, че сме задали правилното
 дефиниционно множество.
Графиката ни показва, че обемът
е функция на х, като х е между 0 и 10,
и изглежда, че достига 
максимална стойност
някъде около това място.
Ще използвам опцията Trace, 
за да намеря приблизително
коя е тази точка на максимум.
Нека да проследя тази функция.
Мога да избера и по-висока, 
и по-висока стойност.
Добре.
Ето там обемът е равен на 1055,5.
След това може да достигне до 1056.
Нека да видим, това е 1056,20, 
а това е 1056,24.
След това се връща обратно на 1055.
Поне като се основаваме 
на степента на увеличение –

Korean: 
y = x (20 - 2x) (30 - 2x)
y = x (20 - 2x) (30 - 2x)
y = x (20 - 2x) (30 - 2x)
 
이제 그래프를 그려봅시다
이제 그래프를 그려봅시다
이제 그래프를 그려봅시다
 
이 그래프는 0 < x < 10 에서 
상자의 부피를 나타냈으며
저 근처에서 최대값을 가집니다
저 근처에서 최대값을 가집니다
그럼 이제 최댓값을 찾아봅시다
그럼 이제 최댓값을 찾아봅시다
 
이 함수를 따라가겠습니다
 
 
이 점에서 1,055.5가 나옵니다
1,056
1,056.2, 1,056.24 까지 올라가네요
다시 1,055로 내려옵니다
그래프를 이용해서

Czech: 
Objem je roven x krát (20 minus 2 krát x)
krát (30 minus 2 krát x).
To se zdá být v pořádku,
takže myslím, že
to můžeme vykreslit.
Zvolím si možnost
vykreslit graf.
Zdá se, že meze
jsme trefili.
Toto je tedy objem jako funkce
proměnné x pro x mezi 0 a 10
a vypadá to, že zhruba někde
tady dosáhneme maxima.
Teď využiji možnosti kalkulačky,
abych zjistil, kde zhruba je bod maxima.
Tak já to zkusím.
Ještě mohu jít výše.
Tady mám
objem 1055,5.
Pak 1056.
Potom tady
mám 1056,20,
tady je 1056,24,
a potom už mám
zase 1055.

Korean: 
그래프를 이용해서
따라가며 값을 찾는 방법도
좋은 근사법이라는 것을 
알 수 있습니다
최댓값은 약 1,056이고
이때 x 값은 3.89 입니다
따라서 x = 3.89 일 때
부피는 약 1,056인 것을 알 수 있습니다
즉 x =3.89일 때
부피가 최대값을 가집니다
지금까지 그래프를 이용해
최댓값을 구해봤습니다
다음 시간에는 미분을 이용해
이 문제를 풀어보겠습니다

English: 
that I have my
calculator right now,
this is a pretty
good approximation
for the maximum value that my
function actually takes on.
So it looks like my maximum
value is around 1,056,
and it happens at
around x equals 3.89.
So it looks like
my volume at 3.89
is approximately equal
to 1,056 cubic inches.
Or you could say that
we hit a maximum when
x is approximately
equal to 3.89.
So far, we've just set up
our maximization problem,
and we've looked
at it graphically.
In the next video, we'll
try to solve it analytically
using some of our
calculus tools.

Bulgarian: 
което в момента съм задал 
на калкулатора –
това е сравнително добро приближение
за максимална стойност на обема, 
до която достига функцията.
Изглежда, че максималната 
стойност е около 1056,
и се получава около х = 3,89.
Изглежда, че обемът за х = 3,89
е приблизително равен на 
1056 кубични инча.
С други думи: функцията 
достига максимум,
когато х е приблизително равно на 3,89.
Дотук просто съставихме задача 
за търсене на максимална стойност,
и я разгледахме графично.
В следващия урок ще се опитаме 
да я решим аналитично,
като използваме методи 
от математическия анализ.

Thai: 
ที่ผมมีในเครื่องคิดเลขตอนนี้
อันนี้เป็นค่าประมาณที่ดีแล้ว
ค่าสูงสุดที่ฟังก์ชันของผมเป็นได้
ดูเหมือนว่า ค่าสูงสุดของผมจะอยู่แถว 1,056
และมันเกิดขึ้นแถวๆ x เท่ากับ 3.89
ดูเหมือนว่า ปริมาตรของผมที่ 3.89
มีค่าประมาณเท่ากับ 1,056 ลูกบาศก์นิ้ว
หรือคุณบอกได้ว่า เราถึงจุดสูงสุดเมื่อ
x ประมาณเท่ากับ 3.89
ถึงตอนนี้ เราได้ตั้งปัญหา
การหาค่าสูงสุดขึ้นมาแล้ว
และเราดูมันจากกราฟไป
ในวิดีโอหน้า เราจะพยายามแก้เชิงวิเคราะห์
โดยใช้เครื่องมือแคลคูลัสที่เรามี

Czech: 
Na základě toho, co říká kalkulačka,
je tohle docela dobrý odhad maxima.
Zdá se, že maximum je přibližně 1056
a nastává někde okolo bodu x rovno 3,89.
V bodě x rovno 3,89 je objem přibližně
roven 1056 palců krychlových.
Nebo můžeme říci, že maxima
dosáhneme pro x rovno přibližně 3,89.
Zatím jsme si tedy připravili naši úlohu
a zkusili se na ni podívat graficky.
V dalším videu se to pokusíme vyřešit
analyticky pomocí diferenciálního počtu.

Portuguese: 
Com base no zoom da minha calculadora,
esta é uma boa aproximação
para o valor máximo
que a minha função assume.
Parece que o valor máximo está próximo
de 1056, cujo valor de x é 3.89.
Parece que o meu volume em 3.89
é aproximadamente 1056 polegadas cúbicas.
Ou você pode dizer que temos um máximo
quando x é aproximadamente igual a 3.89.
Até agora, montamos
o nosso problema de maximização
e o resolvemos graficamente.
No próximo vídeo vamos resolvê-lo
analiticamente usando cálculo.
[Legendado por Pilar Dib]
[Revisado por Miguel Infante]
