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
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!!!
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 👍
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.
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
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.
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.
I know everyone has said this but i was just just like hmmmmmmmmmmmmmmmmmmmmmmmmmmmmm, hmmmmmmmmmmmmmmmm you were you get this i was just so annoyed and confused where this 10L came from even though its supposed to be 20L i thought i was blind or something, but thank god my brain figured it out and yeah
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.
@@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.
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 :)
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😅
Please remove the word "ANY " from your video title. The method you are describing is for solving unconstrained optimization of smooth strongly convex functions.
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.
![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
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
@@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. ❤️
Look for patterns and memorize those patterns so you can apply them to different questions, works for me.
@@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 💀
I have a chapter three test in 32 minutes...... this helped.... still doomed
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐
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
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
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!!!
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.
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐
You are the sole reason I passed my calculus 1 class, Thank you so much
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!!
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
Thank you !! the teacher has been teaching us optimization for a whole week or two, and this helped me understand it much better :)
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
Thanks man your 20s kinda look like 10s tho 😅
facts lmao
My test is tomorrow... been doing not so good in calculus but this helps a bit
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
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
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!! 👍🇬🇧🇺🇸
The math seems wrong when he goes from (40-L/2) * L. Should A = 20L - L^2?
I was looking at the 20L wondering how he got a 10L from 40 divided by 2 😂😂😂😂. Great video though man 🙏🏽
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
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.
pleaseee the description, you're hilarious ahaha and also of course thanks for helping!!:)
Thank you so much! I have a test tomorrow and optimization finally clicked for me in this video!
pov: youre exam is in 8 hours and all skipping is catchign up to you
how did you simplify the original a=wl equation like that i couldnt figure that out
Teat tomorrow on this... Wish me luck! Your video helped a lot, thank you!
hey me too!
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
I have a paper in the morning..this helped ❤
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
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.
this video changed my brain chemistry
Good job of explaining and steps are appreciated. Focus on domain was very helpful.
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
test in 36 minutes but this vid came in clutch
I loved the mnemonic trick
The hardest for me is setting up the equation and knowing the domain
this is gold bro
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
the description killed me
calc bc test in 4 hours, great help!!!
why in the world would you solve for L to start? that gives us an unnecessary fraction
exactly what i was thinking.
Great stuff my guy. I will most definitely be using the smiley face allegory for my math of this topic lol
what about a cone inscribed in a cone
just out of pure curiosity what year of school do they teach this in?
Great video! I love the voice crack haha
Nice stuff, keep it up good sir
AHAHAHHAHA the description
fabulous video
Thank you so much!
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐💐
Thank you so much. This helped a lot.
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
oh yeah he fs knows what he's doing. Great
"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.
thankyou that helped me so much!✏✏✏✏
mate i cba optimaziton is more difficult because its more algebra then calc
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐💐
Midterm in 3 hours wish me luck 🙏😂
Morning of the test baby
Thanks!
GOAT YESSIR THANKS
Damn dawg you distributed that L 💯
i just know u fine
tnx dude this was awesome
great video, thankyou
I was confused because your 20s look like 10s 💀
im sorry but you can tell he's cute by his voice
Bro did not just say you can read this block of text… if you want.
I know everyone has said this but i was just just like hmmmmmmmmmmmmmmmmmmmmmmmmmmmmm, hmmmmmmmmmmmmmmmm you were you get this i was just so annoyed and confused where this 10L came from even though its supposed to be 20L i thought i was blind or something, but thank god my brain figured it out and yeah
thanks
goated
Bro I think I'm in love with you
tysm bro
sad, happy
Bro ngl the skip to 4 is dog water, remake or bad.
you had me until you started skipping algebraic steps
4:22 your “20l” really looks like a “10l”
Aint no way that’s a 20 at step 4 lol
your 2's look like 1's
What
Exam in 30 minutes 😅
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
Thank you so much!
I second that
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐
thanks
your 20's look like 10's...
That’s what I was thinking
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.
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.
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
He divided 40 by 2 and got 10 somehow
It’s 20, he just writes his 20’s a little weird lol
Description is so out of pocket lmao
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 🥹
No calc teacher gives optimization problems as simple as this
Exactly.
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😅
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐
how did u do?
@@slimeball4l540 sadly I had to drop the class😭
@@alexandermbot9467 oh rip
@@alexandermbot9467 lmao
Please remove the word "ANY " from your video title. The method you are describing is for solving unconstrained optimization of smooth strongly convex functions.
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
6:48 got me dead lmaoooo. Super helpful vid man, appreciate it!
lmfao
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)
9:30 smiley 😭❤️
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.
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
The title is very misleading, I thought this is about black-box derivative-free optimization
i have 48% right now in my class on the verge of failing hope I don't die tomorrow
nice caption - ur a king
Taking my final in 15 minutes, thanks
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
Got a final today, Thank God for you!
ruclips.net/video/XPCgGT9BlrQ/видео.html 👍💐💐
yeah man, my final is today . rip
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
what an amazing explanation, also that "good luck on the test" at the end sounded so sincere
Thank you so much ! You’re a life saver
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
The video description😭👏‼️💅✨
Ive been trying to understand this for a while thanks for explaining it in such a simple way.
amazing ...ruclips.net/video/5vnw1YA-gmI/видео.html
Difficult to find an example where you find the maximum and minimum in the same problem. Very helpful thanks.
Thank you so much this taught me more in 10 minutes than my math teacher in 3 hours
Related rates: 💀
Optimization: 😊
Disks and washers: 💀
Work: 💀