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!

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

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

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

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!

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!

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

@lobsidedballs thanks! tell everyone you meet about the videos. EVERYONE!! : )

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.

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

@gumlese what do you mean ' for lectures ' ? i am not employed by a school / college / university

@naras987 thanks : ) I will keep making vids !

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.

@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.

@queenlily2356 : )

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

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

How did you get -3 lambda over 24?

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

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!

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:)

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

@jacobrichards91 ;)

This is awesome. Needed to recall this stuff for application in an upper level graduate course in maths, and this is the first thing to actually bring clarity again. Thanks so much!!

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

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

Dude thank you so much for your help over the years. I signed up to be a patron because you've helped me so much in several of my classes.

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

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

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?

Your videos are awesome! I've been watching them to prepare for a test in multivariable calculus, and although you don't have a video for every topic, you cover almost everything, and in about half the time of other lectures. Even though I haven't had a formal class in multivariable calc, your videos allowed me to learn most of the topics covered in three days. Thanks a lot!

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!

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!

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

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!

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

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

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

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!:)

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.

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

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?

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

@stangman767 thank ya

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

haha! good luck with everything!! : )

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

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!

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

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.

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.

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.

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

how do you keep that sharpie perfect in every video?

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

@krillansavillan no : ) it stands for my tutoring business name 'Just Math Tutoring' which i may soon retire from

what if we wanted to maximise this equation?

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.

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.

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

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

bros 14 years older now

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.

I was trying to understand the math behind the Support Vector Machines algorithm, and it was using lagrange multipliers method because of constraints, you helped me a lot to deal with it in 10 minutes, loves and respects from Turkey :)

you sound like that guy Mr Mackey from south park lol

O.O he's left handed!

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

Hey Patrick, just want to say that you are so great at what you and you really save me in calc. You are the best!

God I hate math

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)

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.

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

Thank you so much patrickJMT for all of your amazing videos! Years ago, I passed the AP Calculus AB and BC exams because of you!

@travelleraroundworld very welcome!

Wow. I wish I would have found you earlier! My Calc final is tomorrow and I've literally just been going through all your videos. This seriously is amazing. It makes a huge difference when you can try a problem and then watch someone do it step by step. Thanks so much!

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

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

This was really helpful. It was precise, and you showed your work very clearly. Thanks again!

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

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

We need more teachers in the world like you. This was incredibly helpful.

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.

amazing stuff. Needed this for microeconomics! A 08 video helping me out in 2022, brilliant

its just incredible how good you´re in explaining ! I JUST LOVE YOUR VIDS! whenever I have a mathproblem, I first make sure if u have done a vid on this topic.... and if so, I can be 100% sure, that I will understand it :) thank u for that !

Thank you so much for this and all of your other videos that got me through calculus.

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

I got a 5 on my AP Calculus BC exam last year because of your videos! I missed a day of my Calc III class (lol, overslept) when my professor talked about Lagrange multipliers. I wouldn't have been able to finish the last question on my homework without your help! Thank you!

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

Thankyou soo much I wasn't able to get this concept you've explained it so well .

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

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 :)

Very powerful u helped me in Mathematics from first year until the final year 🙏🙏🙏🙏

You, along with Nancy (mathbff), have made calculus super duper easy! thank you

Thank you so much. Your notation and explanation was so much clearer than the way my professor drew everything out!

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!

Hey patrick, love your work brother. You're seriously going to get me through the math needed for me EE degree. Just wanted to let you know that I'd love to give all my traffic for finding videos to your site rather than searching it all here, but it's too hard to find. It takes forever to search through all the videos to find what you need rather than just a simple search here. Your old website had things pretty much in the order we learn them here in school, but the new site has moved away

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

Most straight forward and quality explanation on this website

Thanks for showing all the steps, I've come to realize that it's easy to over think problems like this and miss small simple algebra steps! Hopefully I pass this final now haha

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!