LaGrange Multipliers - Finding Maximum or Minimum Values

[CatchPhraseLingo]

thank you so much, you explain it so simply, its perfect!

[patrickJMT]

@CatchPhraseLingo wonderful : )

[137redeemer]

Legen...wait for it.......DAry!

[leah3002]

i love you

[StKamer]

This is better than my colleges in my native tongue!

[apnr19]

Thank you!!! Finally, I got an idea on what to do on our Lagrange assignment! :D

[fzkenya]

THANK YOU! wow, away with lecturers in uni!

[KimJong7hrill]

In my homework I had f(x,y)=3x-2y with the constraint g(x)=x^2+2y^2=44. After solving, my x values were +6 and -6 and my y values were +2 and -2. My question is, how do I figure out the order to put those values into the original function to find the answer? I tried to put them in like f(6,2)=3(6)-2(2) to get max= 14 and f(-6,-2)=3(-6)-2(-2) to get min = -14 and I got it wrong (it's min = -22 and max = 22). Any ideas? My final is tomorrow and this is one of the only things I am stuck on.

[seinfan9]

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

[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

[samehl11]

This was the only topic I didn't really understand for my final tomorrow. You're a life saver.

[lXxxAXMAGxxXl]

Hey Patrick. Isn't it supposed to be f(x,y,z) + k(g(x,y,z) - c)? K being lambda.

Thanks for all the videos btw :D

[system3142]

@lXxxAXMAGxxXl Isn't that the case with a constrained minimization problem which involves inequalities?

[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 !

[ApostasyXVIII]

yeah seriously, i know i've said this before and everyone else on this video has, but i seriously love you. i'm going to find a way to worship you in real life.

[patrickJMT]

@ApostasyXVIII a shrine with some candles works

[katiesmith1776]

This made no sense in class...You taught me how to do it in 5 minutes...THANK YOU!

[dtclaudia88]

and thanks for ure clear and understandable hand writing

[dtclaudia88]

Thanks a lot!!!!

[PCGamerPortal]

what about the hessian matrix?

[TheKawaiiKajika]

thanks man... this really help me..

[lobsidedballs]

I will spread the gospel of Patrick the Great!!!!!

[patrickJMT]

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

[KimJong7hrill]

What if you have three variables (x, y, and lambda) in one of your partial derivatives? How do you go about solving for x and y and then plugging those into the partial derivative for lambda?.

For example I have:

fx = 2x + 4y - lambda = 0

fy = 4x - lamba = 0

f(lambda) = -x - y + 100 = 0

If I solve fx to get one variable on the left I will end up with two on the right. Then it just gets messy when I plug that variable into the partial derivative for lambda. Please help anyone :)

[JdkParkour]

Dude, I fucking love you

[travelleraroundworld]

Thanks for putting a minimum example - it unlocked my thinking that whenever we use LaGrange method we need to find a maximum. Thank you!

[patrickJMT]

@travelleraroundworld very welcome!

[LAnonHubbard]

All through the video I though it was plainly obvious that all the TVs should be made in factory A. Then I did 6(90^2) and compared it to 6(60^2) + 12(30^2) and saw the latter was a lot smaller. Facepalm! Thanks Patrick - I just wanted an introduction to Lagrange multipliers and this was fantastic.

[gumlese]

@patrickJMT haha thanks, it might not be a fast method but it certainly works like your videos!

[drumline064]

Thanks so much for this. Calc 3 seemed impossible until I found your vids. Keep it up!

[gumlese]

@patrickJMT Sorry it was meant to be past tense, I thought you taught at the lousiville and vanderbuilt universaties. I was just wondering which method you used to teach because it seems to work. I did a maths course last semester which used powerpoint slides and relied on your videos for comprehension (which I thank you greatly for).

[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.

[gumlese]

@patrickJMT for lectures do you use slides or a projector and go through material like you do on video?

[patrickJMT]

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

[lolliholic256]

@patrickJMT what does it mean when a contradiction occurs?

[kx32ta1]

@patrickJMT I hope its because you are making a living with youtube and that you didnt get fired. (if I remember correctly you were teaching not to long ago)

[patrickJMT]

@kx32ta1 ha, no i did not get fired. : ) i quit

[tsg162]

the Bob Dylan of math

[patrickJMT]

@tsg162 let me just say, i do not care for bob dylan. i would like to like him, but i just can not.

[AssassinsCreedVids]

you are AMAZING. THANK YOU!!!

[inspectorsufyan]

Dude, you know what? You are a genius.. I wish you were my professor.. Anyway, do you have any lecture on optimization by differentiation?? I'm really having hard time on this topic.

[lolliholic256]

@inspectorsufyan he does, just search around a little bit.

[rightyourwrong]

you should work out harder problems in your examples. Like ones where the system of equations doesn't work out so well. or where there are multiple critical points. that shit always gets me...

[ondra38]

Thank you so much! It really helped me a lot. I really suck at maths and this made it a little easier for me. Thank you.

[mliniman]

lol I like how you say lagrange. Lagraaaange

[queenlily2356]

A hero. A hero, I say!

[patrickJMT]

@queenlily2356 : )

[anderscarlsson21]

Thx, very useful. Do you have videos for second-order conditions for max and min as well?

[meakos]

Thanks, this help me a lot.

[Milioo93]

Thanks so much :)

[sugarvenom435]

thanks for the help! definetly good review for my third year microeconomics class

[sugarvenom435]

thanks for the help! definetly good review for my third year microeconomics class

[challebbe]

wow!!! thank u for this video... i've learned a lot... =)

[cbusoh21]

why is he subtracting f(x,y) and lambda g(x,y) and not adding them?

[lolololort]

@cbusoh21

It's equivalent (your landa = - his landa), but It makes more sense to say minus if you look at how this formula came about.

[jamieclarke321]

mind=blown...subscibed.

[PatronRick]

At our school, we learned a different agorithm, but it's all the same thing really. (Setting grad(f) to lambda*grad(g) and g=k) and then 2 more steps for specific cases

[0554844777]

i need a more involved book in mathematics and calculus and statistics. in theories and so on. i need to get more involved in it. but i couldn't find any in my country please help me :)

[Keya82]

thanks a lot, now i unterderstand langrange :)

[solelytocomment]

you are seriously the LaGrange to my Multipliers <3

[ilovetvb]

nice stick people drawings :)

[yucky1336]

dammit youtube I accidentally refreshed the page I dont want to see another AD!!!!

[tamubasketball]

is there a video of this but instead you are finding the maximum?

[onimusha542]

You know what? The Calculus book I use goes about solving lagrange multipliers in a different way which confused me. Then I found this video and an epiphany happened.

[ThisReallySuckz]

You are brilliant, man! You remind me of the great Herbert Gross from MIT (1968-1973).

[selimm11]

thnaks



[SalamiWurscht]

patrick, you should put a flattr and donation button on your website :)

[vonlsh]

correct me if im wrong, im quite new to this topic...so im guessing the 3 variable one would be using the same procedure? so instead of having F(x,y,lamda) like in this case, u'd have F(x,y,z,lamda)?

[tthanh92]

''lameda''

[owninit1]

I have a Calc final tonight, and I'm learning off all your videos. My college professor is absolutely TERRIBLE so I'm learning off your videos. HA YAH! THANKS!

[someoneusedmyuser]

you just saved my ass. i have a test tomorrow and i had no idea how to do this :)

[scepticpatriot]

impossible to understand with my college book , but hopefully you made a video about it !!! :)

[MechEngineer111]

You are THE MAN!!! ive been struggling to do la grange for like 2 months now and its nearly exams. i thought i was screwed! watching this 10 min video i could answer all the questions easily!! Thank you very much <<from Mechanical Engineering student from New Zealand.

[schwarzegarde]

Wow, that was easy to understand. Thanks for the video, greetings from germany!

[Mayitzin]

You're the Chuck Norris of Math.

[kkc1648]

You and Sal are both good men. My lecturer is just damn lousy compares to you.

The lecturers in uni don't know how to teach. Very sad. They are too relax in their office thinking of tricking students without proper explanation. This is the man. Rock.

[owenzarido]

Thanx for your help ! But i want to ask if u can make a video on how to solve functions with (x,y,z) ?

[owenzarido]

Thanx for your help ! But i want to ask if u can make a video on how to solve functions with (x,y,z) ?

[ahmadhuneidi]

please answer this cause alot of people have been asking it, what do u do differently if you want to maximize your function?

[Channel4Four]

seriously, they should put your face on money you're so good!

[colexionztelar]

nice job my friend

[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.

[kkal0]

great video! the left handed writing was a bit unnerving though :)

[kkal0]

Great video! The left hand was a bit unnerving but you explained it really well.

[sidiqmk]

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

[BeBattey]

Patrick, why are you subtracting the lambda part of the equation instead of adding? In the end it doesn't matter whether you add or subtract it because it equals 0, but is there something I'm missing?

[h0wud0in2]

yeah but that is just an application and makes use of less than basic calculus. I was wandering how do you derive this result...

[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 :)

[ZodarH]

Can only echo the comments of many other users. Excellent explanations, very helpful for me (Economics student)

[selbs91]

You taught me more in ten minutes than my college Calc prof has taught me all semester. Muchos gracias.

[stivio00]

thanks man

[jophis66]

patrick, are you a mormon?

[simianmirror]

Thankyou thankyou thankyou! Your method is infinitely easier than the method I have found in any text books

[simianmirror]

Thankyou thankyou thankyou! Your method is infinitely easier than the method I have found in any text books

[alborzgod]

Fuck these Mormon ads

[UnFisicoMatematico]

I´m Mexican, but I have a question for you...

How you record your videos? for example, where you put your camera for not move?

[success2508]

THANKS A LOT ...

[SLNProductions]

Thankyou soo much. The textbooks are not nearly as helpful as you are. Great job!!!

[Ugapop]

seriously, im a german economics-student and learn this from an american guy! :D i like the way you explain things. its very useful! best regards from germany.

[patrickJMT]

@Ugapop see how nice usa people are

[omgwtfmk]

dear mr. lagrange, I HATE YOU AND YOUR MULTIPLIERS and i wish to constrain you

on the other hand, mr. JMT, i love you. you have saved my life 5! times and you will exponentially continue to help me throughout my life.

[Adammysorewala]

Awesome video my man. helped a lot

[Androopy1]

you and salman khan should join forces and take over the maths tuition universe

[batuhany]

You are a life savior. Thank you so much.

[yarie18]

Thank you so much for this , I really understand this stuff now

[erenaksu1234]

I wanted to ask the same thing. Why is the formula not + Lambda ?

[Tbarber2112]

why is it minus lambda and not plus?

[rerikm]

I got 3 words for you: I LOVE YOU!!!!

[patrickJMT]

@rerikm : )

[MrKyte12]

Wow!! you are amazing! tomorrow is our final exam in math and I dont really understand a thing.. but thanks to you.. Everything is clear now. Thank you so much..

[bla7091]

Actually filling in the equations isn't too hard... the proof seems rather complicated though

[interpolitic]

thank you very much, greetings from Turkey . .

[WalkerDestroyer]

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

[Agentasian77]

Dude thanks! Keep it up

[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.

[patrickJMT]

@naras987 thanks : ) I will keep making vids !

[matics19]

@naras987 Honestly, I completely agree. I go to class, write down the title of the lecture, then come and search these videos and the ones on Khan Academy and learn from those!

[isla2974]

that's a very nice video indeed. I did not even require to wear my headphone. Thank you.

[hendsem]

use the lagrange's multiplier to calculate the minimum and maximum volume of a woman's breast F(x,y,z)=2X+y^4-5z under the constraints between D cup and DD. (5marks)

[katinkaschyberg]

THANX!!! :D In 10 min you explained what took my professor a whole lecture ,and i still didnt get it.

[meteorologyswimgirl]

Just wanted to say thank you for posting these. My prof. teaches from the book and the book is very confusing. Your videos helped me pass calc 2 and have already helped me immensely with calc 3.

[carmensq9591]

thank you soooo much, you saved me!!

[luqukoman90]

Thanks a lot. I pray for your success in future.You saved me a lot.Thanks for the easiest explanation on earth.Thanks.Thanks.Thanks

[fvboss429]

thanks a lot for these videos, in this one can we compute this equation to get maximums or minimums ? or we can only define it by doing that final test?

sorry for my english

[patchesohola]

u learn me goods

[beethz]

thank you for teaching me lagrange, must easier to learn when you can play and pause and hear what your saying.. unlike my prof.

[MomImHungry]

Thanks so much pal! reduced my stressing to a minimum for my final!!

[kareneley]

You probably just made me pass calculus, thank you sir!

[GooseyFruit]

dude i just went on your site .. u have.. everything....:O

[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)

[carlo8921]

Thanks a lot! I've been having a lot of trouble with understanding this. You're really helpful!

[MrMikevandyke]

Yo man! i cant seem to find the vid on how to deal with 3 variables??

[MrMikevandyke]

Yo man! you say at the end u r going to upload a vid on how to deal with 3 variables? I cant find it! is it up?

[AlBaShA13]

thanks! I have an exam in an hour, and I had to idea about this subject..now I am good at it! thanks to your help!!

[RebSMP]

u're awesome.. it really helped me... thanks and keep up the good work ; )

[88Anit]

Thank you Patrick!

[xryuuseix]

I'm really confused as to when you would subtract or add lambda... this video shows to subtract lambda when we want to maximize--what's the case when we would ADD lambda to f(x, y)?

[Theravhard]

best teacher in the whole of youtube!!! keep doing ur thing!! 

[yumyum210]

just wanted to say man, i've been watching your videos ever since calc I and have never watched one of your videos and felt like i still didn't understand something. im almost done with my minor in mathematics and to be honest, i think i would've quit trying to be an engineer a long time ago if it wasn't for you. keep it up!

[sasamuraki]

awesome!

[duhduhduhduhduh]

After watching about 5 of your videos, I realize you're left handed. =D

Anyway, you taught LaGrange Multipliers better than my book ever could. Thanks very much!

[JohnAntonyFortune]

could you explain why you set Fx, Fy, and more importantly Flam to zero? thanks

[mluetten]

Great Stuff! Maybe you can get your camera to face the paper from a better angle or even get a digital pen and notepad! Keep up the good work!

[fabooster]

Thank you so much for posting these videos! None of my maths professors or their aids could explain as well as your simple and concise videos do! =)

[masterjim2007]

Great Example

[greyfoxxelite]

I would be sooooo screwed without you!

[jaredtkatz]

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

[scdlbrdr]

What if your constraint is a less than or equal to or a greater than or equal too? can you still use this method?

[Julman75]

excellent video, as usual Patrick!

[gregorioster]

WOA! thanks for the teaching!

Great, good, nice, excelent teaching... good teaching... yeap.

[idolgin776]

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

[Pocky99Eater]

The love for math is returning to me)) Thanks!

[mvaredi]

Thank you, you helped a lot to understand the concept using this nice example.

[deen2dam]

superb , you saved my time

[xhinandoa]

beautiful....thanks

[vsahanarao]

the teaching is really good, very easy to understand.but if u could give the geometrical explaination also it wld have been good.

[patrickJMT]

@vsahanarao well, cant do it all in a short video

[whysocurious92]

god bless you man :'(

[lifetech2]

nice vid bro ;)

[patrickJMT]

@lifetech2 thanks!

[amrichbiatch]

dude .... yo the man .... bro..... just did a crazy exponential function saddle point question using one of yo videos as a guide ...... thanks !!!!!!!!!!!!!!!!!!!

[sssssantiagooooo]

to verify if the critical points i've obtained through this method i've always used the second derivative criteria, or the hessian criteria. And it's not so dificult at all.

[ohgeeitsph4rrah]

i understand this now! thank you SO much!!!

[stangman767]

that was great. good teaching

[patrickJMT]

@stangman767 thank ya

[DJGrayMusic]

I love you. You are superior to my actual professor.

[popoable1]

thanx hey i totally get it now.

[badboy4life414]

You have made a mistake in your procedure,although the solution is correct..

[Revanv]

thank you so much, you have really helped me so many times

[MrDrinkBeer]

Thank You Patrick!! Awesome Video!!

[redechoes]

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!

[arixue]

What if i wanted the max ?

[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.

[krillansavillan]

thanks patrick, i watched this video about a month before i learned it in Calc 3! it really helped. Your the man.

and by the way, does JMT stand for the group Jedi Mind Tricks?

[patrickJMT]

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

[krillansavillan]

@patrickJMT why's that pat?

[BPColin]

@krillansavillan hahaha i thought the same thing! jedi mind!

[this1ssteve]

this video was very helpful. you sir are the reason im doing good in my cal 3 class. i really appreciate you taking the time and effort to post all these videos and sharing your knowledge with the rest of us. for some reason the way you break all this down makes me understand the subject matter so much better.