I suffer from the same problem... I feel like its because we overthink that we get something wrong. But even if we try our best to not overthink, we'll end up being paranoid about if we are/aren't overthinking that we will end up overthinking anyways.
In calculus there are two things I gave up on learning, related rates and optimization. No matter how much time I spent on them I never got it right and I thought that there was no hope for me. This video is the first video ever that actually helped me understand how to do optimization. I think I still need to do more practices problems, but I genuinely want to thank you because I finally get it now. So truly from my bottom of my heart, thank you. ❤️
@@ghostgoingdark_ ABSOLUTELY DISAGREE. Optimization are definetly the easiest. Related reates are just so fucking complicated I literally skip them on the exams because I know I won't even get it right. Optimization isn't that bad though for me.
@@nopoyiik You need to practice. Start with the easier problems then move onto the harder ones. Draw a graphic, note down all the given quantities, note down the rates that are given and the rate that you're trying to find. Assign variables to the things that change as a rate. Write down all the relevant equations/formulas for the problem. *DO NOT* plug in any quantities until after you've implicitly differentiated the equation and manipulated it so that you're solving for the rate that you're trying to find. It's easier to understand if you differentiate and write down the rates using Leibniz notation.
@@JasonJia11 wish you would’ve replied to this a lot sooner. The only problem I skipped on the final exam was the related rates 😭 I practiced everything but that, I honestly gave up on it. I still got a 128/140 (the related rates problem was 12 points). It was a little painful to leave it empty, but it’s whatever. I passed and that’s what matters
Writing for comprehension purposes 1. Draw the function 2. Write the area function and constraint function 3. Solve constraint function for a variable 4. Plug variable function back into area function 5. Find critical points using first derivative test 6. Check if critical points are extraneous 7. Check critical points that aren't extraneous using second derivative test 8. If a maximum, you have your answer for that variable
@@valyahmadi that's the equation for the perimeter-- area is w*l, but because we are finding the dimensions of the enclosure based on the amount of fencing around the space (40 feet), you would need to use 2w+l=40. The reason it is 2w+l instead of 2w+2l (the standard equation for perimeter) is because one side of the enclosure is the wall of the house, so it would not be necessary to find a length of fence for that side of the enclosure. Hopefully this makes sense :)
I had been having SUCH a hard time with this for months, but now it's the night before the AP exam and this video has officially taught me how to do optimization problems!!! The part about having to only have one unknown variable so that that is what the derivative is in terms of is ingenious and I am SO thankful to have that advice now!! Thank you so much!!!
Related rates is easier because you deal with only one equation most of the time. These usually take a main equation and one or more helper equations that the constraint goes into (most of the time). A lot more thinking and planning involved. The calculus itself is the easy part.
I think they are equal. Related rates has like 5 different equations total depending on the situation but optimization you have to make your own equation although they are usually more simple
I love how you say we are not in multivariable calculus yet. So relatable hahaha. Optimization and Related rates are hell. Optimization is the big boss I am dealing with.
Yeah I feel you, my calc 1 class is getting consistent means of 40% on our exams at purdue, dont stress and you'll get through your schooling just fine 😌
@@UltimitShadelord thanks I got a B in calc 1&2 this year. As long as your around 50% you should be able to bring it up. Algebra messed me up so that’s what I focused on. Helped a lot. Good luck 👍
@@mads2158 I did optimization in precalc as well. There’s an algebraic way of doing this but imo it’s more convoluted than calculus. It gave me an appreciation for derivatives lol.
man thank you so goddamn much, this is a life saver. everyone who did the exam yesterday tanked the optimization question, hopefully, I wont after watching this!!
in calculus 2 too .. The video here in YT is simplier than the word problems given in school. That is why, it is still hard for me to answer my module with all those videos that I've watched.
Very helpful, I just still struggle with finding some derivatives, but it help me understand the optimization of problems, hope I get a good grade in my test today😅
Studying for my calc final :) optimization is actually kind of fun and so is calc haha...I love being able to understand math. Thank you for helping! I feel like I can ace optimization now (as long as they don't throw in a problem where there's some crazy area formula...oh well, confidence confidence lol)
It's a way to be sure of the answer. When evaluating the critical points, if the 2nd derivative is negative at f(c), you know that you have a max value at x=c, due to it being concave down. And vice versa if the 2nd derivative is positive.
It’s crazy how everyone is studying on the same day as their final or a day before, I am doing the same but it’s a nightmare that I hope it won’t repeat.
Well explained bro, as a super-simple introduction to this whole topic!! I like the little mnemonic with the ‘smiley’ / ‘sad’ faces, that’s a nice one to teach!! 👍🇬🇧🇺🇸
This is setting a new standard. I read a book with a similar theme, and it set a new standard for me. "Unlocking the Brain's Full Potential" by Alexander Sterling
Hi, this seems to work for some optimization problems. But, what about multi stage, non linear, multivariable, systems subjected to different set of constraints. For example trajectory optimization, or maximum volume of a box with the minimum area defined by a set schematic. The second one could simply use the Langrange multipliers with programming. But the first one?
Thank you. My class switched teachers during this unit and no one isn’t he class ha notes on it and it’s not on her site. So this is literally saving me before I retake the exam
Please remove the word "ANY " from your video title. The method you are describing is for solving unconstrained optimization of smooth strongly convex functions.
the interval should be [ 5, 20 ] , and not [5, 30] . Since 2w + L = 40 , then L = 40 - 2w, , the maximum w can be 20 because 40-2(20) =0 and if you go further than that, you would get a negative number. and the minimum it can be according to the requirements is 5 . With that in mind, the maximum area is 200, and the minimum area is 0 ( if you use all 40 meters of fencing on one side). Thank you for the video.
![How to Solve ANY Related Rates Problem [Calc 1]](http://i.ytimg.com/vi/gBHIZlF0TX8/mqdefault.jpg)
![How to Solve ANY Related Rates Problem [Calc 1]](/img/tr.png)
The derivatives thing and that stuff is fine, but it's just creating the equations that's so hard for me
exactly my problem too... finding the critical points are the easiest parts of optimization imo
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@@johncena3022 Never would I have thought the hardest part of calculus for me would be reading and Algebra....
@@CocoaThunda so true
I suffer from the same problem... I feel like its because we overthink that we get something wrong. But even if we try our best to not overthink, we'll end up being paranoid about if we are/aren't overthinking that we will end up overthinking anyways.
In calculus there are two things I gave up on learning, related rates and optimization. No matter how much time I spent on them I never got it right and I thought that there was no hope for me. This video is the first video ever that actually helped me understand how to do optimization. I think I still need to do more practices problems, but I genuinely want to thank you because I finally get it now. So truly from my bottom of my heart, thank you. ❤️
@@ghostgoingdark_ ABSOLUTELY DISAGREE. Optimization are definetly the easiest. Related reates are just so fucking complicated I literally skip them on the exams because I know I won't even get it right. Optimization isn't that bad though for me.
@@nopoyiik You need to practice. Start with the easier problems then move onto the harder ones. Draw a graphic, note down all the given quantities, note down the rates that are given and the rate that you're trying to find. Assign variables to the things that change as a rate. Write down all the relevant equations/formulas for the problem. *DO NOT* plug in any quantities until after you've implicitly differentiated the equation and manipulated it so that you're solving for the rate that you're trying to find. It's easier to understand if you differentiate and write down the rates using Leibniz notation.
@@JasonJia11 wish you would’ve replied to this a lot sooner. The only problem I skipped on the final exam was the related rates 😭 I practiced everything but that, I honestly gave up on it. I still got a 128/140 (the related rates problem was 12 points). It was a little painful to leave it empty, but it’s whatever. I passed and that’s what matters
The first two sentences describe my week perfectly 💀
Once related rates clicks for you you're going to wonder how it was ever difficult
was staring at the 20L thinking "how tf did he get 10" for like 5 minutes... lmfao
Bro how did hr
@@maak289 It's a 20 he just wrote it like a 10 lol. Took me a second too
@@beb3891 NO WAYYYY LMAOOO I WAS LITT TRYNA FIGURE A WAY TO GET 10 FOR THE LONGEST😭
same haha
Writing for comprehension purposes
1. Draw the function
2. Write the area function and constraint function
3. Solve constraint function for a variable
4. Plug variable function back into area function
5. Find critical points using first derivative test
6. Check if critical points are extraneous
7. Check critical points that aren't extraneous using second derivative test
8. If a maximum, you have your answer for that variable
Do you know how he got 2*w+L = 40, wouldnt the area just be w*l
@@valyahmadi that's the equation for the perimeter-- area is w*l, but because we are finding the dimensions of the enclosure based on the amount of fencing around the space (40 feet), you would need to use 2w+l=40. The reason it is 2w+l instead of 2w+2l (the standard equation for perimeter) is because one side of the enclosure is the wall of the house, so it would not be necessary to find a length of fence for that side of the enclosure. Hopefully this makes sense :)
How do you check if points are extraneous? Number line?
@@CalebMathews-yz7qe you find the domain and see if the number you find is in the interval
I have a chapter three test in 32 minutes...... this helped.... still doomed
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1 year later but me too:p
How did you do???
I also have a chapter three test in 38 minutes lmao
Final in an hour lol
I had been having SUCH a hard time with this for months, but now it's the night before the AP exam and this video has officially taught me how to do optimization problems!!! The part about having to only have one unknown variable so that that is what the derivative is in terms of is ingenious and I am SO thankful to have that advice now!! Thank you so much!!!
Related rates is easier because you deal with only one equation most of the time. These usually take a main equation and one or more helper equations that the constraint goes into (most of the time). A lot more thinking and planning involved. The calculus itself is the easy part.
I think they are equal. Related rates has like 5 different equations total depending on the situation but optimization you have to make your own equation although they are usually more simple
I love how you say we are not in multivariable calculus yet. So relatable hahaha. Optimization and Related rates are hell. Optimization is the big boss I am dealing with.
You are the sole reason I passed my calculus 1 class, Thank you so much
Thank you! Quickly and concise explained this....having my class online has been difficult 😪
I feel you bro, I have 71% right now in mg chemistry class
Yeah I feel you, my calc 1 class is getting consistent means of 40% on our exams at purdue, dont stress and you'll get through your schooling just fine 😌
@@UltimitShadelord thanks I got a B in calc 1&2 this year. As long as your around 50% you should be able to bring it up. Algebra messed me up so that’s what I focused on. Helped a lot. Good luck 👍
Currently watching this before a test at this point I'd happy with a C.
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No calc teacher gives optimization problems as simple as this
Exactly.
This has been extremely helpful, since optimization has been one of my weaknesses in PreCalc H. I’m now ready to ace my final exam!
you're doing optimization in precal?? I didn't even learn what a derivitive was until calculus
@@mads2158 I did optimization in precalc as well. There’s an algebraic way of doing this but imo it’s more convoluted than calculus. It gave me an appreciation for derivatives lol.
Literally have a final tomorrow for calc and I never ever got optimization but this video def helped out. Wish me luck guys
how did it go bro
@@xiraei guess not good
got a calc exam in a few hours too wish me luck 🥹
what an amazing explanation, also that "good luck on the test" at the end sounded so sincere
Thank you !! the teacher has been teaching us optimization for a whole week or two, and this helped me understand it much better :)
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Thanks man your 20s kinda look like 10s tho 😅
facts lmao
man thank you so goddamn much, this is a life saver. everyone who did the exam yesterday tanked the optimization question, hopefully, I wont after watching this!!
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I swear optimization is the hardest topic in calculus 1
the examples here on the internet are pretty easy. I dont fkn know why my uni has to make everythign so hard
in calculus 2 too .. The video here in YT is simplier than the word problems given in school. That is why, it is still hard for me to answer my module with all those videos that I've watched.
Optimization and related rates are literally the worst
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This is saving me for my first calculus final at college! Thank you!
Difficult to find an example where you find the maximum and minimum in the same problem. Very helpful thanks.
my friend watched this half an hour before she had to take her calc 1 test & she got this specific problem right
My test is tomorrow... been doing not so good in calculus but this helps a bit
The math seems wrong when he goes from (40-L/2) * L. Should A = 20L - L^2?
6:48 got me dead lmaoooo. Super helpful vid man, appreciate it!
lmfao
how did you simplify the original a=wl equation like that i couldnt figure that out
Very helpful, I just still struggle with finding some derivatives, but it help me understand the optimization of problems, hope I get a good grade in my test today😅
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how did u do?
@@slimeball4l540 sadly I had to drop the class😭
@@alexandermbot9467 oh rip
@@alexandermbot9467 lmao
Studying for my calc final :) optimization is actually kind of fun and so is calc haha...I love being able to understand math. Thank you for helping! I feel like I can ace optimization now (as long as they don't throw in a problem where there's some crazy area formula...oh well, confidence confidence lol)
Why do you need to find the concavity? After the first derivative it seems like i have all the necessary info to finish the problem
It's a way to be sure of the answer. When evaluating the critical points, if the 2nd derivative is negative at f(c), you know that you have a max value at x=c, due to it being concave down. And vice versa if the 2nd derivative is positive.
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I am confused at 7:14, how does 10 - L = 0 mean that L is 20? Wouldn't L be 10?
its a 20, his 20's looks like 10's
@@mrfishyman5725 thanks 👍
his solution is wrong
Got a final today, Thank God for you!
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yeah man, my final is today . rip
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your 20's look like 10's...
That’s what I was thinking
He divided 40 by 2 and got 10 somehow
It’s 20, he just writes his 20’s a little weird lol
It’s crazy how everyone is studying on the same day as their final or a day before, I am doing the same but it’s a nightmare that I hope it won’t repeat.
Thank you so much this taught me more in 10 minutes than my math teacher in 3 hours
Sir , Were you not supposed to take area but in solution you have taken a surface area.
i missed class and this was really helpful. thank you very much
9:30 smiley 😭❤️
For the concavity I always thought of concave up and l looked at the “u” in up to know that it was a min when I was first learning it.
Ive been trying to understand this for a while thanks for explaining it in such a simple way.
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pleaseee the description, you're hilarious ahaha and also of course thanks for helping!!:)
I was looking at the 20L wondering how he got a 10L from 40 divided by 2 😂😂😂😂. Great video though man 🙏🏽
Isn't it that you can treat A(l) as a quadratic equation and found its maximum point directly without derivation?
Well explained bro, as a super-simple introduction to this whole topic!! I like the little mnemonic with the ‘smiley’ / ‘sad’ faces, that’s a nice one to teach!! 👍🇬🇧🇺🇸
This is setting a new standard. I read a book with a similar theme, and it set a new standard for me. "Unlocking the Brain's Full Potential" by Alexander Sterling
Teat tomorrow on this... Wish me luck! Your video helped a lot, thank you!
hey me too!
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The video description😭👏‼️💅✨
why in the world would you solve for L to start? that gives us an unnecessary fraction
exactly what i was thinking.
Thank you so much! I have a test tomorrow and optimization finally clicked for me in this video!
Write your 2s better bro. I thought you were writing a 10 for like half an hour and then had to redo my whole worksheet because i was confused.
legend bro, hearing this explanation really makes a big diff
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what about a cone inscribed in a cone
i have 48% right now in my class on the verge of failing hope I don't die tomorrow
Where did the 10l come from?
Hi, this seems to work for some optimization problems. But, what about multi stage, non linear, multivariable, systems subjected to different set of constraints. For example trajectory optimization, or maximum volume of a box with the minimum area defined by a set schematic. The second one could simply use the Langrange multipliers with programming. But the first one?
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Calc 1 bro...
Great stuff my guy. I will most definitely be using the smiley face allegory for my math of this topic lol
What happens if L wasn't on the domain or is L always in the domain.
What do you do if you don’t take 2nd derivative test? Like you said it can be very hard sometimes.
i dont understand how you found the domain (5,30)
just out of pure curiosity what year of school do they teach this in?
i live in california, usa and im doing this in my sophmore year of high school
The title is very misleading, I thought this is about black-box derivative-free optimization
nice caption - ur a king
Thank you. My class switched teachers during this unit and no one isn’t he class ha notes on it and it’s not on her site. So this is literally saving me before I retake the exam
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Description is so out of pocket lmao
FINALLY someones that can make this make SENSE
Please remove the word "ANY " from your video title. The method you are describing is for solving unconstrained optimization of smooth strongly convex functions.
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If the there was 40 fence how did we only use 30 for max are makes no sense
test in 36 minutes but this vid came in clutch
I have a paper in the morning..this helped ❤
TY bro. Ive been rusty w calc but this made sense
You made everything even harder to understand. Or maybe I'm just too dumb for calc.
you are never too dumb for anything you are smarter than you think and you CAN achieve anything
Really nice and easy problem. Keep it up 👋🏼
It's wrong, l+2w = 40 and we need to find [l*w]max. So l and w should be in 2/1 ratio. answer we'll get is 355.55. way bigger than 200
Good job of explaining and steps are appreciated. Focus on domain was very helpful.
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Taking my final in 15 minutes, thanks
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pov: youre exam is in 8 hours and all skipping is catchign up to you
This is actually very helpful. Thank you!
Thank you so much ! You’re a life saver
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kiss me because you are better than orange chemistry tutor
mate i cba optimaziton is more difficult because its more algebra then calc
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The hardest for me is setting up the equation and knowing the domain
"ANY" optimization problem? So, discrete, dynamic, ... , really "any"??
The problem you show is static, differentiable, concave ...
you got me there! I just meant in the scope of calc 1.
the interval should be [ 5, 20 ] , and not [5, 30] . Since 2w + L = 40 , then L = 40 - 2w, , the maximum w can be 20 because 40-2(20) =0 and if you go further than that, you would get a negative number. and the minimum it can be according to the requirements is 5 . With that in mind, the maximum area is 200, and the minimum area is 0 ( if you use all 40 meters of fencing on one side). Thank you for the video.
yeah noticed this too, I knew it was weird
Nah, it's still [5, 30]. The question says the width has to be at least 5 feet long. 2W+L=40; 2(5)+L=40; L=30
This video is simple and explains the math very well!
isnt L = 10?
Nice stuff, keep it up good sir
Midterm in 3 hours wish me luck 🙏😂
this is gold bro
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I loved the mnemonic trick
calc bc test in 4 hours, great help!!!
the description killed me
5:29 u got me trippin that shit was not a 2, that looks like 1
all goes well until u have a different constraint and dont know what to do with it
College bad. This channel good
this video changed my brain chemistry
I was confused because your 20s look like 10s 💀
need more questions
So, not ANY optimization problem; but just single-variable optimization problems.
Thank you so much. This helped a lot.
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thankyou that helped me so much!✏✏✏✏
AHAHAHHAHA the description