❖ LaGrange Multipliers - Finding Maximum or Minimum Values ❖ 

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!

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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!

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

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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:)

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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!

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!

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

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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

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

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

@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.

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!!

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.

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

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!

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

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

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?

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

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

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

haha! good luck with everything!! : )

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!

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

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

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

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.

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!

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.

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

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

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.

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

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?

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

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.

bros 14 years older now

how do you keep that sharpie perfect in every video?

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.

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!

How did you get -3 lambda over 24?

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

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

Most straight forward and quality explanation on this website

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you sound like that guy Mr Mackey from south park lol

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

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

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.

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.

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

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Its amazing how you explained something in less than 10 minutes that took my university math professor 2, 1.5 hour lectures and still confused half the class.

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

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.

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

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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!

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Concise yet covered all I needed. Thanks.

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!

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