❖ LaGrange Multipliers - Finding Maximum or Minimum Values ❖

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@dchill4086]

One thing you forgot to mention is how much harder math is when you can't hear the sharpie noises. Seriously though your videos are awesome and the sharpie ASMR is legendary. Thanks!

[@youtune8453]

Omg i cant believe im trying to study something who explained 13 years ago, almost when i was 5 yrs old Ok before watching the video i read your comment you are so sweet sir... I have a question my lecture explained somewhat in different manner she said F=f+ lambda pie Where F is what we have to find f is constrained eqn Pie is function My question is how to say which is constrained eqn and which is normal eqn,In question i can see two functions I hope you will reply its been sooo long this video got uploaded And i think this msg will notify your previous videos Waiting for your reply sir!!!!

[@tinyasira6132]

that's so kind 😊 we should all help each other ❤

[@AzikIlhom]

Thanks

[@patrickjmt]

sometimes i watch my own videos when i forget how to do stuff! i can summon my old powers!

[@Hi_Brien]

I also tend to go back to old videos when I need a refresher! I randomly was asked to tutor since I'm a math major at the library, and they were like "working on Lagrange multipliers" I was like "Minimum? Maximums? How'd that work again?"

[@Hi_Brien]

@@prince29999 there are two ts there, I'm a lover of math who wears a hat.

[@Hi_Brien]

@@prince29999 but it is getting better :)

[@4b1saisrinivas2]

13 years

[@Goku17yen]

@@4b1saisrinivas2 😂

[@patrickjmt]

u did a good job old me! i remember now! thanks!

[@AtikaTahsinSaba]

Wow XD

[@mocha6315]

@@AtikaTahsinSaba you know this video is very old when the comment itself is 12 years ago lmao

[@SquidwardsMoney]

Patrick, I'm sure you've heard this thousands of times already, but your videos are nothing short of amazing for saving peoples' grades and explaining concepts. Thanks so much!

[@geenstagni1060]

Gosh I absolutely owe my life to you! I simply cannot believe that I was able to learn something that was 77 slideshow slides and way over my head through a single example in less than 10 minutes!! Sincerely, thank you SO MUCH for what you do for students!

[@patrickjmt]

Glad I could help! come back any time :)

[@wk961]

dude, i've been watching your videos since my first college algebra class ten years ago in community college. Now, I'm getting my engineering master's and I'm taking a class in numerical optimization. I literally couldn't believe you have a video on this obscure topic! Thank you.

[@travinator99]

congrats on your journey

[@Foxoq]

One day I'm gonna graduate and send you a cheque. Thanks Patrick. Edit: Yes I graduated. 😂

[@patrickjmt]

+Jordan S you can donate a dollar a month and patreon and i would be happy :)

[@sanjaykrish8719]

Patrick I am in India. Is there a way to donate to you in rupees

[@m13m]

Sanjay Krish yeah debit card

[@xmj1279]

Jordan S feels👍👌👌✋✋✋✋

[@DioGTGaming]

Jordan S did you graduate?

[@anthonyaddo]

Incredible I learn in ten minutes what a professor bumbles along about for two hours.

[@roslin8060]

Well, that's probably because it's accompained by a whole bunch of formal math theory, not just a recipe on how to calculate exercises. :P

[@stephaniecurry45]

Ros Lin I mean this is more useful honestly

[@WilliamSprecher]

Dont be afraid to plug the site! Keep plugging! Keep the paper there longer!

[@patrickjmt]

+Willballhead ok, good idea, i will

[@tripleS9000]

Thank you. I never comment on videos but you literally cleared up an entire semester's worth of confusion from my econ class. Prof introduced this but never went in anywhere near as much detail in solving this as you have.

[@tiffanysteytler627]

Patrick, i passed my calculus exams because of your videos. I went from literally 3% to 52%. I am enjoying maths and it's all because of you. you not only make maths fun, but it's easy to comprehend and remeber. thank you:)

[@Frixos000]

I love you dude.... you have saved my ass in so many exams

[@sydneystraver]

Honestly wouldn't get my business maths without all these videos! Thanks for everything!

[@lifewithdylan]

I will pass the maths side of my degree thanks to you! if your ever in London ill buy you a pint or 10

[@patrickjmt]

hoping to be back there one day :) congrats!

[@t0lg4drc15]

Did you pass your exam? :D

[@leskipbayless3280]

@@t0lg4drc15Check his videos he got one of the best grades in his year group at University

[@freeway7979]

I have had many math professors taught me but Patrick is the far better teacher than any professor I have ever had. Thanks a million!

[@kwanele1253]

WOW, its started like boring, but i told my self i have got to pay attention. WOW, very nice explanations, clear in my mind. indeed so confident at the moment. THANKS A LOT

[@vasundharasontakke6503]

the explaination is so crisp and clear and you handwriting is so clean, all of this makes it look so simplem thanks

[@GajuGatera]

You might have just helped pass my exam tomorrow! Thank you so much!!!

[@georgeanons301]

Patrick ---> Fast, to the point, learning with full information (great for cramming) Relevant practice problems that help you understand the material. Khan ---> Conceptual intuitive explanations. Good for in depth understanding. Also good to prime you for Patrick's videos. Textbook ---> Reading math is impossible.

[@philipwest2551]

Thanks for the video: I think that when you obtain 12x - Lamda = 0 and 24y - Lamda = 0 you should simply note that 12x=24y or x = 2y and substitute THAT into the third equation. It's a lot easier in this case!

[@bryanaustin22]

ive been watching all of your videos throughout my college career. you are the best math teacher i have ever seen. thank you so much

[@patrickjmt]

thanks so much, i appreciate your kind words :)

[@olyadmulisa6825]

so you dont know if you are minimizing or maximizing ? you have to do a trial and error?

[@PaperAdept]

I think I love you. 10 minutes and you made all of that make sense, a feat neither my professor nor my book could do.

[@patrickjmt]

@gumlese oh yes, i did used to teach at those places. i never used slides or a projector; i always hated that method as a student. but it was the traditional ' writing on the board and talking ' method. not the most effective i think honestly, but that is how they wanted it done.

[@aeaeae13]

Like alot of other people, I got my exam tommorow morning and it's currently 2 am. Gosh, you've helped alot of people over the decade what a nice feeling that must be!

[@Shafique96]

On similar videos and other examples I see a positive sign when setting up the lagrange? ( f(x,y,z) + L(g(x,y,z)-k). And other times I see it set up like how you showed in this example. Are both ways acceptable?

[@amymantilla9685]

wow you're still helping people even in 2021! I've been struggling with this concept for weeks now and after this video i finally understand wtf im supposed to do LMAO king.

[@patrickjmt]

thanks for helping! i get sooo many questions a day, i just can not answer them all! : )

[@autogordel]

patrickJMT making this world a better place with his free knowledge. And making my gradelist better. Thanks so much man.

[@kushagragupta97]

If we have exactly the same way of finding maximum or minimum , and if lagrange's multiplier gives the minimum of a function but we have to find its maximum how do we do that? Like if in your example we have to find maximum cost How do we do that?

[@NikicaJEa]

also my thought

[@nirojkhatiwada8689]

X=59 y=31 my guess

[@AncientWord1]

Can't stop feeling grateful to you. U made me understand this thing so easily. In Kenya,, am thankful

[@modibacm2783]

How do we know if it's maxima or minima?

[@messididit]

you are actually helping people you probably have never expected of. thank you so much!

[@Norbizzle2012]

My professor never liked LaGrange Multipliers because of the nasty system of equations that could arise. Instead, he taught us to turn the function f(x,y) into a function G(x,y(x)), G(x(y),y), or G(t) by using the constraints or through parametrization and ending up with a function G of only one variable. In this problem for example, using the constraint, you could say that y=90-x and that G(x,y(x))= 18(x^2)-2160x+97200. Using the first derivative test, you come to the same conclusion that 32400 is a min of that function. There are obviously times when you can only use LaGrange Multipliers, but if it is possible to use this method, it is much easier.

[@lebeobachter]

Norberto Torres while this is really a more effective way in this case, it is not always possible to express one variable as a function of the other

[@danielgates7559]

Actually for this example you can just use Cauchy-Schwarz Inequality and destroy this problem instantly...

[@Maximo10101]

You make it so easy. I was reading my lecture notes, my tutorial notes, the Calculus book, scratching my head for an hour. Watch your video for a couple of min and it makes sense! Keep up the great work!

[@LaverneADavid]

How did you get -3 lambda over 24?

[@GooseyFruit]

your a very good teacher man, straight to the point and with no accent, gotta love it! keep up the good work, highly appreciated(y)

[@000Achmed]

lol way to help me figure out in 10 min what me and my teacher couldn't do in a couple days

[@and1fer]

If you hadn't done those couple days of trying to figure out, you must probably wouldn't understand it. Everything counts. That's reason why we go to lessons although our teachers might not be that good.

[@naras987]

PatrickJMT, you are the savior of many a calculus student. You are a superior teacher to tons of professors including top tier schools. Please take these comments as motivation to keep providing quality instruction to the masses. seriously, these are great.

[@JorSex]

Awesome video. I have one question, sometimes i've seen: f(x) + λ(constraint) instead of f(x) - λ(constraint) Is there a difference?

[@abdullahshukri9430]

It's just a constant..

[@madameneruda]

you're the freaking of tutoring Patrick. Thanks a million for what you're doing

[@NitishDobhal]

nice one that explains HOW (not why) it works! :)

[@dtranscend]

Dude I know that you've heard this a million times, but thank you so much. I've had pneumonia this semester and missed over 3 weeks of class. I would be retaking calc III next fall if it were not for you and your amazingly concise videos. Actually I've found that I seem to get a more intuitive grasp on these concepts learning from your videos compared to classroom time, and the combination of both is absolutely outstanding. You've saved my bacon and I will recommend you to everyone. THNX!:)

[@DANGJOS]

how do you keep that sharpie perfect in every video?

[@fahadovich]

lol

[@squiresuzuki]

(the important questions)

[@Jurkblot]

Insane that 16 years ago I could have been watching this but instead I was 5 watching Fred 😔✊🏼

[@poetryaddict1]

The way he says "Lagrange" sounds like the way that one Vine says "Lebron James" lol

[@carlbrovsky7500]

Lagranjames

[@huolong437]

If Nirvana were a French band: Le Grunge

[@Salamanca-joro]

Thats how all teachers say it😂

[@jamesblu1146]

I'm looking at all these comments from 2 years ago, and I just wanted to say that your videos are helping me pass calculus3 in 2018. Cheers Patrick

[@izzyxyoung]

Wow, I just realized I could use this to diversify my stock portfolio better. Thanks so much!!

[@EagleLogic]

TheDarkKnight2124 Well you could create a function with let's say two variables. z = ax + by where a and b are constants. a represents the price of stock a and b represents the price of stock b. x and y is the stock quantity. Say you desire 90 stocks. You then have x + y - 90 = 0 for lambda. z = ax+by for your main function. Then you can proceed with the methods from this video.

[@WalkerDestroyer]

One of the only tutors on youtube that can give khanacademy a run for it's money.

[@mortalas100]

You do not subtract the constrant , you add it to the original function.

[@YoungColCol]

You can do either since G(x,y)=0 (x+y-90=0)

[@dinosoup]

Most straight forward and quality explanation on this website

[@patrickjmt]

haha! good luck with everything!! : )

[@kendylharvey660]

Thank you so much for actually explaining step by step what you are doing to solve the equation. I have watched so many videos that don't explain key parts in solving it and it's been very frustrating. You're awesome!

[@pd7009]

what if we wanted to maximise this equation?

[@TheBossStuart]

Petr D look at the function. Making more TV A's (x) is more expensive than making TV B's (y). So just make 90 tv A ;-)

[@jankaas9256]

Maximising applies to other equations. For example an equation for Profit. Maximising this function is no different from minimising a function. Its always the same: (the function you want to min- or maximise) - λ x (constraint).

[@Moonwalkerdrey]

this video was uploaded 10 years ago and here i am learning from you. thank you so much!

[@HT-rq5pi]

Is there a video explaining the concept/proof behind this method? I can apply the brute force method behind solving this, but I want to actually understand this - i've tried looking up various websites but they are too complicated as they prove general results for n dimensions.

[@samajapstaceht]

Look up a course on the calculus of variations. You'll probably need some analysis training, but that will tell you all that you need to know.

[@brenxbux]

go to class

[@HT-rq5pi]

i'm not a college student, I am learning from home.

[@brenxbux]

i skip so much class i thought you did too xD

[@awitzk]

Hey man. A very basic explanation is that this method finds the points at which the gradient of the constraint equation (direction of maximum increase) matches the gradient of your objective equation. Imagine level curves of the constraint equation and the level curves of the objective equation on the same graph. This method scales the constraint equation to where the directions of maximum increase are equal. Its easier to see if you re-write the method as (Gradient)F= lamba*(Gradient)g. F being the objective function and g the constraint.

[@sruthikagrandhi2740]

Hi i just saw ur video it helped me a lot i got all my questions clarified thank you 😊. I just saw that it was uploaded 15 years ago i was in shock

[@Risate]

bros 14 years older now

[@yrnkevinsmithC-137]

16 now

[@hejhowareyou]

I play you videos while listening to slowcore because you voice is so soothing.

[@francistembo650]

you sound like that guy Mr Mackey from south park lol

[@bachstrad644]

Thank you for all your help. Every time I watch one of your videos I click on the google ad. This is my way of donating to you :)

[@eff700]

O.O he's left handed!

[@treylitefm]

You've taught me more in this 10 minute video than I've learned in the last two weeks of calc. Thank you, bro. You're a lifesaver.

[@jaredtkatz]

this is awesome. i go to MIT and this video makes more sense than the professor's lecture. Thanks a ton!

[@donaldwilson3579]

God I hate math

[@garytuortojr7338]

You don't even know how helpful this is. I have only taken up to Calc 1 but am currently back in school pursuing a master in economics and in my Micro class we used lagrange for consumer demand theory and I was just completely lost thanks so much for this! The partial derivative stuff threw me off but they're really just the same thing as a "regular" derivative.

[@Simmiebird]

Best Lagrange explanation in KZbin thank you.

[@craig5716]

My calc class keeps getting smaller and smaller every week, and class averages are hovering around 58%. I'm just smiling there knowing I got Patrick to help me out. Best tutor/TA and it's free.. unreal!

[@prudenciojoaomuchanga7267]

This video was posted in 2008 and it's 2018 now and it is still of great help! Thank you Patrick!! :)

[@KingBueno619]

My professor taught me this today and skips so many steps. This video is very clear and very understandable. Thanks Patrick!

[@Zerpyderp]

14 years later and i still watch ur vids, thanks amigo

[@shen1266]

I want to thank you for how i survive math classes because of your videos, thank you so much 💖

[@scycon21]

Simply an amazing teacher. I left lecture thinking "What the hell was that" and I come to KZbin to find Mr. patrickJMT and now I am confident!

[@Lamorak117]

I just wanted to thank you for the help. I'm still working on Lagrange Multipliers but this video helps a lot. We have to use these all the time for my upper division Economics course and my professor did a terrible job at explaining. So thanks again!

[@cegley21]

Thank you for your videos. You talk nice and slow, and actually explain things! You are quite literally saving my grade!

[@oexnorth]

perfect perfect perfect. My textbook does not explain it at all like this. Now it seems so much easier. Thank you.

[@pulechishimba9502]

you explained it better and made Lagrange multiplier easy to understand. best Lagrange multiplier tutorial

[@hurolinci5986]

Why do you make me understand it so easy whereas at uni they make it look so hard... Cheers mate!

[@davidfield5295]

Excellent explanation, it's very helpful that you walked through an example instead of just presenting a conceptual framework

[@SplatterBacks]

Your videos are great refreshers of material we covered a long time ago that has since become a little hazy. This is great stuff, thanks a bunch.

[@effortless35]

The maximum cost will be on the boundary (specifically y=90). Technically we should have checked (x=0,y=90) and (x=90,y=0) too, I think.

[@patrickjmt]

no, i have not done that particular example, or any others with lagrange multipliers. perhaps i will make one tomorrow though!

[@lowekygoodlooking434]

Im so happy that theres people like you here that can teach me some real math

[@Mathiology]

YOU ARE AMAZING ! I always watch your videos and learn from them , and I always recommend my friends to watch your videos. I don't know what to do without you !! MAY GOD MAKE YOUR LIFE LONGER !

[@dhanushgopan4957]

Thank you for making it this simple

[@arber622]

Taught so much better then my uni prof who gets 100k+ a year and my textbook that cost 150$... He might as well just show your videos in lectures, thanks so much @PatrickJMT !!!

[@cupcake6054]

You Made My Day , 13 years Ago But Still Helping Others

[@drrhobert]

There is a flaw in the proof in 1:43-1:46 and 7:52-8:48. In principle, the stationary point (x,y)=(60,30), i.e, where the gradient vanishes, could have been a saddle point, and therefore neither a maximum nor a minimum. To finish the proof, one would therefore have to check the boundary cases (x,y)=(90,0) and (x,y)=(0,90) as well.

[@metasameta236]

You have no idea how helpful this is. Thank you so much

[@patrickjmt]

Glad it was helpful!

[@rosuchoach704]

you are awesome Patrick. I'm from Bangladesh, and your videos help me understand maths more than my typical class lectures.

[@idolgin776]

Thank you...I needed a refresher on Lagrange multipliers and your video was great!

[@superman3621]

i never thought i would say this but...you make math FUN!. honestly, thank you.

[@xLashesToAshesx]

This came up in my exam today, wouldn't have had a clue if it wasn't for this video. Thank you!

[@lokithor83]

i've studied this topic years back but due to negligence, i've lost it.. i found it back today clearer than ever.. thanks..

[@sfcsarah]

Thank you so much, not just for having a clear explanation but for also showing a good practical example. :)

[@albert275]

Holy shit, 10 minute video trumps my hour long lecture on Lagrange multipliers. Thanks man!

[@21esanch]

Ive been watching your videos since i was in calculus 2 no words can express how grateful i am to u111 thnks man!11

[@seinfan9]

Up all night studying for my vector calculus final in the morning. You rock, dude!

[@abhijitnayak5445]

the best optimisation in engineering teacher I hv ever come across

[@austinsouza5002]

You just made my life so much better, I can't tell you how much i appreciate this video