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
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 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!!!
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 :)
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 👍
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.
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)
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!!
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😅
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!! 👍🇬🇧🇺🇸
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.
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.
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
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.
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
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?
![How to Solve ANY Optimization Problem [Calc 1]](/img/logo.svg){kind=logo}
