Optimization Problem #5 - Max Volume of a Box Made From Square of Material
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- Опубликовано: 9 сен 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Optimization Problem #5 - Max Volume of a Box Made From Square of Material. In this video, I find the maximum volume of a box made from a 2ft x 2ft piece of metal when corners of equal size are removed and then the sides of the box are folded up.
So I loaded this video up this morning, but had to leave to go take my calc final before I had time to watch it. There was 1 question on my final that I couldn't figure out and it was literally the exact same question as in this video... fuck my life.
ghty102 but did you pass?
If there was only 1 question this China man couldn't figure out. Then..
6 years later, but did you pass?
@@user-yq4eq5cy8d Calc 3 ended up being the worst grade on my undergrad transcript (and I took more math beyond it). I can do calculus in my sleep now, but I still have the occasional nightmare from this class. Luckily my major was Computer Science, so I awake from those nightmares on a very comfortable mattress! :)
@@ghty102 good to hear, Im taking computer science next year too!
Oh my gosh! I was so confused on optimization problems, and I have my calculus final tomorrow. I'm starting to get more clearer on them thanks to your videos!! Thank you so much! :-)
I watched your videos last night because I had no idea how to do problems like this or how to use the chain rule but you make it so understandable. I felt really confident with my Calculus exam today.
No worries, 3 times 4 is a lot harder to figure out than calculus. Like these problems are nothing compared to 3 times 4 lol
EH GO JETS! FK THE BLUES
dude you save my life literally every time i have to do any calculus work. my prof is a total dbag so luckily i have you to teach me. thanks a lot man
Thanks Patrick, this helped a lot for understanding the concept. Now only if there were a video for the 100s of other types of problems, I swear Optimizing has to be the most annoying sub chapter in all of 12 Calc.
Haha I love how you just fly through taking derivatives and doing complex optimization problems, but then you hit 3x4 and get stumped for a minute. =). Great video btw, helped alot.
"Unless youre a bad box builder !!!" LOL. Good sense of humor.
"What is 3x4? hmm whats 2x4..Wait what am i doing ? 3x4 is 12" LOL thanks so much for making these videos, even if it was super early in the morning, when you're not quite awake yet. This means a lot to us Calc students. :)
Gosh, I'm so thankful for this video! I'm a Computer guy, and this in Cal 3 was burning me out!
this channel saved my life
right there, at 2:12 i stopped to give you a thumbs up. Seriously patrick, you're really gifted at this teaching thing.
WHY IS THE HEIGHT IS JUST X ?
An Nonymous ME TOO HAHAHAHA
You sir... are my tutor/helper/Nerd god. Your videos have helped me understand Calculus to the MAX!
Thank you. I just passed the cset subset 3. I’ve never taken calculus but I watched all your tutorials and they helped me a lot. I studied for about 200 hours Thank you.
congrats!
Times like this I just wonder how previous generations did it, without help from the internet! Thanks to channels like these and other free resources! Graduation in a month and I owe it mostly to u guys Khan Academy You Tube Google patrickJMT
michyswaga So true! Internet is a bless :)
+michyswaga I find myself thinking this ALLLLL the time while I'm studying :D
It's because they didn't. Our generations education is 3X more difficult than Gen X. My parents never even learned calculas.
Can't have 0 or 1 as values for x, the values can be in between but not inclusive:
0
5:30 lol brain fart, just proves how hard we rely on memorizing our time-tables instead of intuitively computing them. Thanks for the vid!
i think im gonna pass my test tomorrow :3
George Thompson did you ever pass
George Thompson did u pass it
The anticipation is killing me. Did you pass it or what
I have a final tmrw
Clo4ken G did you ever passed?
"3 times 4 is uhh lets see, well 2 times 4 is...what am I saying?" xD
And just like that I think I have found my new Calculus professor. Thanks!!! For some reason optimization always confuses me but now I feel more confident about it.
My calculus final is tomorrow, and I have an A in the class and no real trouble with it. However, your videos make an awesome review. Thanks man, keep giving nerds a good name :p
Glad to see that someone who loves math as much as you do still has little brainfarts about simple stuff like the multiplication. I do this sometimes and it's like wtf I KNOW THIS lol. Good to see someone else does it.
OMG CALCULUS IS STUPENDOUS (as much as how amazing your explanations always are)
Thanks for your comment, I looked up the foil method and now it makes sense (well a little sense anyway). I don't really need maths now I'm doing a BA design course but I do still want to work on my maths as it is defiantly my biggest weakness (along with electrical theory!!)
@Spacexchild super happy that i could do that for you : )
Look at 02:14. The white space he points to that says "side" will be folded from its horizontal position into a vertical position. Now that white space is standing straight up, so x becomes the height of the side of that white space. Since it is a box all the sides are the same height, so x becomes the height of the box.
Thank you for working hard for us. GOD bless you.
God bless you and anyone else who is good at math.
Patrick is my lord and savior before every calc exam
i bless thee
Thanks alot man you explain it so well and easy to understand, you are a legend for helping me out!!! :)
thank you sooo much. i dont know how much I can thank you
lol at 5:31.
Good job tho! It was really easy to understand.
More fun if you angle the sides, you get two quadratic equations that feed a solution to each other
THANK YOU DUDE YOU SAVE LIFES HERE
@AceAites happy to help : )
That was a great explanation! Thanks!
shouldn't it just be less than one since length can't really be zero either?
Thank you! This was very helpful!
Splendid. Thank you very much
oooooo, i finally see it visually why v(1) wont work. THX A LOT
The minimum surface/volume is a sphere
The maximum volume of a box is a cube
To get a cube from a square you divide the edge by three and notch away
It took longer to write that than to think it
I hope derivatives are useful in more complex ways that are themselves useful
Don't mind me... :)
Thanks a lot...
greetings from germany
Thank you soo much this video was soo helpful...
@ICarnag3I glad i could help : )
THANK YOU SO MUCH FOR THIS
@VongolabossX The height of the box is not necessarily the same as the length or width.
thank you
Don't worry I was doing the problem ahead and got stuck on 3*4 too XD
Thanks for the vid btw!
Thakn you sooo much !!
Find the volume of a renctangle when the SA is given
how to solve optimization problem when the SA= 2000 cm^2 is given, and I need to find the the volume.
Please help me
Jim
Thanks for uploading; excellent video! The only thing I don't understand is what is the connection with the derivative; why does it work to take the derivative?
@ 5:27: "what is 3x4... well lets see, 2x4 is uhhh... what am i saying, OMG 3x4 is just 12. Its verrry early here." HAHAHA
I need the method of the measuring cylinder
@negativesplits06 I'd say that general solutions and optimization problems are the hardest. General solutions were by far and away the hardest I thought. I think that general solutions is like an intro to diffy Q
Thankyou
@millamulisha I understand you're joking but I feel like answering anyway...
#1 It says in the problem description that they are squares.
#2 If they weren't squares the box would have different heights, effectively meaning it is a pretty useless box...
Thanks alot!!
You should be endorsed by Sharpie :)
5:30 i know that feeling lol
thanks for making math easy :)
Hello! Am a proud youtube student of yours, Hahahaha. Umm, may I know what textbook you use in the former vids? I am in dire pain for a good reference in Calculus, -aspiring eng student.
Thanks @patrickJMT
@nutcraker2002 yep :)
great man great!
find the dimensions of the rectangular box open at the top of maximum capacity whose surface area is of 108 square. inches ? please explain this problem
@magazines823 thts....wat he did. factoring is just a fancy word for dividing.....
Do a optimization problem involving a circle or a cylinder or a cone. Something using pi
That would help thanks..
So, if you were only given the volume first, say it was 4000, would you end up writing the equation as 4000 = (y-2x)(y-2x)(x) and then solving for Y?
The proof should be 2/3 to the power of 3, right ? I think you forgot to see that it is 1/3 of 2 feet or 2 feet divided by 3. So it should be (6/3 - 2x2/3) (6/3-2x2/3) 2/3
I have a question. At 0=4-16x-12x^2, couldn't you factor 4 out and have 0=4(3x^2-4x+1)?
:-) Thank you!!
Related Rates and Optimization are by far the 2 hardest parts of Calculus 1.
FACTS
I really don't get it...it has nothing to do with the math, but I can NEVER set these problems up...ever
thanks
I need help we’re doing this in class but I’m in precalc and we’re not allowed to use calculus yet how do I solve this
Shouldn't you just cube the length of one side?
What if one of the square corners has a value of 2x+1, with my length as 15 and width as 12? What should be the volume?? Our teacher gave us this question and i have no idea how to solve it T^T
Did you donate as a token of appreciation?
Why to find the critical points of the equation?
a factored then used the ac method to find the x intercept one of my values was 1 the other zero
how can you divide by four when you set your derivative equal to 0 ?
I have this exact problem except I have no values for the sides of the sheet of metal . help please !
well you dot the same step but you remplace the 2 by your X
Does this mean that the maximum is equal to the minimum, if not, then how can I calculate the minimum?
The minimum would be the endpoints, which would be 0.
im gonna ace my midterm tomorrow
youre awesome!
Second derivative show what???
I dont understand where (8x) comes from. Surely 2x * 2x = 4x ???
Can i send you a problem similar to this? I'm so confused
if the sides that she's folding is X I don't get why the whole height of the box would be X....wait idk maybe I'm not thinking about it right. can someone explain?
this maybe a weird question but uhh, do you not have a pinky on your left hand? lol
once you plug in your zeros shouldn't it equal 0 again
he plugged it into the original equation
Philosophical question here: how do you know the little cut parts are supposed to be squares? >.< lol jk jk. love me some calculus. In DiffEQ and loving it!
(2-2x) and if x=1 then 2-2=0. What the hell ? you must choose bigger number than 2 for the sides.
why did we divide by 4, I didn't get that part patrickJMT
+Sylvia Okonofua It's just like factoring out 4, but it is to help factor.
Is not x should be greater than 0 because at 0 height remians no more
Nobel Prize📡 kab milega???
This sort of helped except for when you said times the top and bottom and last part, you should have being more clear.
calc is easy. 3 times 4 is another story.
hahha that was soo funny when you couldnt figure out what 3x4 was
does anyone know how to prove this??
3*4? oh difficult :D