lagrange multipliers, three dimensions one constraint (KristaKingMath)

[@shyambatman3101]

This is the only tutorial video whose auto-generated subtitles perfectly match with actual ones. That reflects Krista's clarity in her voice. Cheers.

[@shyambatman3101]

Yes Dude, that's absolutely right

[@shyambatman3101]

Except C instead of Z in one case.

[@bongfinance6779]

Your channel is a life saver.I did one semester worth of maths in 24hours.This channel is amazing.

[@kristakingmath]

Thank you so much, I really appreciate that!

[@PrashantKarmakar]

When subjected to the given constraint, the maximum value of f is 1. This maximum value occurs at the four points (1,1,1), (1,-1,-1), (-1,1,-1), and (-1,-1,1). When subjected to the given constraint, the minimum value of f is -1. This minimum value occurs at the four points (-1,-1,-1), (1,-1,1), (1,1,-1), and (-1,1,1). There are eight critical points which satisfy the given constraint. Since the question only asks for extreme values and not the points where those extreme values occur, the given answer is correct for this specific case. But in general, leaving out valid critical points will lead to wrong answers. I hope this clarification helps someone who has the same confusion.

[@siyabongathokozanishiba6950]

This is by far the best explanation of the three dimensions constraints ever, far better than my already paid up lectures. Thank you so much Krister

[@evat267]

Krista you are a LEGEND

[@shivam-tiwari19]

at 5:22 why is there no plus or minus on the x, y, and z? if you take the square root of all three sides of the equation, why don't you need to account for the fact that x can be -y which can be -z for example?

[@bbd9353]

i think so too, and f have 8 place not 2

[@ayanavroy8269]

I believe you're right, solutions like (1, -1, -1) and (1, 1, -1) would work in this case. Though, the actual extreme values still don't change: they are 1 and -1.

[@abdurahmanitani5982]

as always, i search the internet to find good multivariable calculus videos i am always let down until i get to Krista's channel, she never lets us down. thank you ! awesome video as always

[@abdurahmanitani5982]

i also had a question what if we had only one critical point, how do we know if its a maximum or minimum ?

[@nico3727]

@@abdurahmanitani5982 old but you can find any point that fits the constraint then put into fxyz and if f is a higher then you know the critical point is a min

[@hassankhalid2753]

you are simply the best! how can I live without you!

[@ElonMust00]

your channel is life saver i swear.

[@ElonMust00]

this vid deserves more likes.

[@maryann1ization]

Omg, I wouldn't have survived 3 semesters of calc without you!!!! Thanks!

[@kristakingmath]

Aw thanks! I'm glad I could help along the way.

[@guitarttimman]

I took 4 semesters of it and OWNED the curve way back when I was in my early 20's. Everyone wanted to kill my hippie white ass back then. That was a long time ago, and I was competing with people from all over the globe. I OWNED in calculus, and can you guess what University I attended? It was Purdue University which was one of the leading schools of science and math at that time. Uh, I won scholarships and received PELL GRANTS. I also worked full time. Oh and guess what else? I was a high school drop out who was only armed with a G.E.D.. I didn't learn how to read until I was 19 years old, but I have this mystical ability in mathematics and science. With enough money and resources, the sky is the limit. I could invent anything. I don't have a photographic memory. Damn it. But, I do have a talent for understanding how to figure out seemingly impossible to solve problems.

[@guitarttimman]

Have you ever taken linear algebra? Differential equations? I owned in those courses too.

[@guitarttimman]

My instructors used to say, "TIM! WHY AREN'T YOU WORKING FOR NASA?" ha ha

[@ledzeppelin4892000]

Has anyone told you that your voice is so soothing, when it comes to Calculus? It really makes the entire subject much easier to get through. I so wish I could pay for your lessons but I'm just a poor college student =\

[@kristakingmath]

+Juan Gonzalez No worries, I'm just glad the KZbin videos are helping!

[@augustinechapuswike7121]

Thank you.you have proved to be so very helpfu especially to distance students like me.

[@rockyshepheard6054]

At 2:12, why isn’t the partial deriv of f wrt x equal to x...since y and z are treated like constants?

[@valor36az]

Although the question is 3years old someone else might be wondering, the variables of f(x,y,z) are multiplied it’s like saying the derivative of 5x=5

[@ginaocegueda6718]

Thanks Krista. You really helped me on my Calculus III homework problem!

[@kristakingmath]

You're welcome, Gina, I'm so glad it helped! :)

[@arshad3491]

You saved my life many times Thank you I appreciate it

[@kristakingmath]

You're welcome, Arshad, I'm happy to help! :)

[@aliamirallana]

just one question x^2=y^2=z^2 wont that also give other possibilities; i mean other than x=y=z as we take square roots?

[@mastera50]

Yes, you cannot ignore the negative roots when taking the square root.

[@guitarttimman]

Thank you. I'm glad you cover a lot of areas. I truly do enjoy your videos. You're very smart.

[@osamaabushama]

Hi Krista , new presentation, quick question on tool used, how can use the white chalk pointer ,? I tried skecthbook and could not get that white chalk.

[@kristakingmath]

The white chalk is an image I made myself, and I add it into the video with my editing software. I don't do it in Sketchbook.

[@coolclips101]

I'm skeptical of the reasoning used here. As others have mentioned, there were other critical points that weren't accounted for in this process. Also, we can't divide by lambda without showing that it is always nonzero.

[@travisbrooks6604]

by definition, lambda cannot be zero ever man. if it could be zero you could never solve as all your f gradient things would be set equal to zero.

[@tajpa100]

You are a great professor

[@kristakingmath]

Thank you so much, Antonio! :)

[@Islanders1932]

When you take the square root of x^2=y^2=z^2 isn't it technically + - x=+ - y = + - z? Like couldn't (1,-1,1) be a critical point as well as (-1,1,-1) and so forth?

[@chaitanyachaitanya4051]

Your lectures are really amazing and very helpful. clears all the doubts in a student's mind, I wish i had a teacher like you in my college!

[@kristakingmath]

+Chaitanya Chaitanya I'm so glad I could help!

[@maxwelllohss8047]

If you divide by lamda, you must account for the case where lamda equals zero. If lamda = 0 Then (x*y*z) = 0 Note: with constraint, only two variables can be zero. Example: if x=y=0, then z^2 = 3. Therefore, your solution does not account for the critical points: (-+sqrt(3),0,0) (0,-+sqrt(3),0) (0,0,-+sqrt(3)) It just so happens that these values are no local max or local min values, but in many cases, they will be local max or min values.Besides that, great video! You are a very skilled teacher.

[@NiggaSlayer666]

nerd

[@OMRIGREEN-xw3he]

@@NiggaSlayer666I’m sure you’re proud of this comment 5 years later.

[@michaelregalia2539]

I was thinking the same thing thank you

[@trm_tba9820]

you're the best, krista

[@FlyingRaptor123]

Just got an A on my test! Thank you for your vids!!

[@kristakingmath]

That's so awesome! Congrats Ivan!

[@uborkaemberd7738]

With a three dimensional function, is it no longer possible for a critical point to be a saddle point?

[@Balvantkurveti25]

Love this channel 💗

[@aethox]

Doesn't going from x^2=y^2=z^2 to x=y=z leave out the points (-1,1,1), (1,-1,1),(1,1,-1), (-1,-1,1), (1,-1,-1), and (-1,1,-1)? Also in case you have not been made aware since posting this video, those are not necessarily "critical points" at the boundary, since the derivative of the function at those points is not necessarily zero.

[@omardelacruz9442]

Gary Wilson hater

[@guitarttimman]

Do you even understand how gradients work?

[@soumenmaity7410]

If there exist one value of x,y,z. Then how we know that at that point the function f has maximum or minimum??? Please describe this case.

[@kitsVideo]

Your videos that I have seen have been amazing. Very helpful. Thank you.

[@kristakingmath]

So glad you like them!

[@KCIsMe]

Your videos are really helpful, but I have two questions. Why didn't you use all of these points (-1,1,1), (1,-1,1),(1,1,-1), (-1,-1,1), (1,-1,-1), and (-1,1,-1) ? and how can you tell that one of them is a maximum and the other is a minimum. How do you know that both aren't mins or maxs or that one or both are saddle points?

[@wilveryescas4166]

+Karan Chopra on the last part she mentions that since x=y=z so if x=1 then y=1 and z=1 hence (1,1,1) and the same with the -1

[@7Z7A7C7K7]

+Wilver Yescas but x = y = z isn't correct. It should be plus or minus x = plus or minus y = plus or minus z

[@wilveryescas4166]

+Z Plymesser 2x2=2y2=2z2 ->we need to simplify this to the simplest form so lets divide the whole thing by two this gives us x2=y2=z2 ->in order to get rid of the squares (and the plus and minus)we will be taking the square root of the whole thing which gives us x=y=z and you get the positive sides because all three of them are variable on the other hand if you had x2=25 in this case five is a constant then x=+-5 the same way if x2=y then x=plus or minus y

[@wilveryescas4166]

+Z Plymesser just solve this and you will see the realtionship if x=y and y=sqrtof x then what is y

[@LucasSoaresy]

where is the constraint function localized in the graphic? Is it like inside the graphic of the f(x,y,z)? I'm Sorry if I wasn't clear, I'm brazilian and your videos are being very helpful, but sometimes I don't get it all.

[@hamadhalbahrani8781]

deep thank and big appreciation for your effort and hard work in order to help students

[@pawerybacki98]

When going from x^2 = y^2 = z^2 to x = y = z, why did you assume positive solutions only? I could be wrong, but I think it would rather be |x| = |y| = |z| , which gives us 2^3 = 8 critical points, including something like (1, -1, 1).

[@pawerybacki98]

Oh, that's because x^2 = y^2 = z^2 = 3.

[@alpha563]

Love from india mam! Hats off to you ❤️

[@kristakingmath]

Thanks, ALPHA! :)

[@ademolaadebowale2723]

My only question is why are we allowed to divide by lambda and assume it's a non-zero, but not consider the case where it is zero and find the critical points that result from that path.

[@andreamonge5025]

Thank you so much for your videos! Your way of explaining is truly great and have been life saving!

[@kristakingmath]

+Andrea Monge I'm so glad I can help! Thanks for letting me know.

[@robertoberidojr.435]

A bigger number doesn't signify automatically a local maximum, the same with the lesser number, doesn't necessarily mean a local minimum. How could we prove that these are really the maximum and the minimum?

[@hulkstrong2389]

What program are you using for your blackboard background? Love your videos by the way!

[@kristakingmath]

Thanks, Michael! The background program is Sketchbook by Autodesk. :)

[@sriharshaananthoju8671]

i think x=+-1,y=+-1,z=+-1 are the correct values

[@guitarttimman]

Don't think. Test.

[@lorenzomyersjr.5824]

VERY HELPFUL!

[@mauosante9537]

Hello, I have one question, if the value of f(1,1) and the value of f(-1,-1) it the same, is it a maximum, minimum or neither ?

[@kristakingmath]

+Mau Osante They are either both LOCAL maxima, or LOCAL minima, and there is no global max/min.

[@thbitaan7]

Which software/app are you using for writing?

[@kristakingmath]

+Tania Hazra It's called Sketchbook :)

[@clairepilgrim6310]

what if the max/min equation was (xyz)^2 how would you determine whether it was a max or a min? thanks!

[@somarya4519]

pretty good way to describe. Love from India

[@fwright22]

you're a saint. god bless you.

[@kristakingmath]

I'm just glad I can help!

[@fwright22]

lol you have. Almost done with Calc III thanks to some of your videos!

[@Sarkaari_Shayar]

if i have only one extreema then how can i check is it maxima or minima???

[@kristakingmath]

You still just check one point on each side of the single extrema, and then if you get positive on the left, negative on the right, it's a max. And if you get negative on the left and positive on the right, it's a min. :)

[@geniusmathematics9123]

👍👍 fantastic Thank you so much

[@kristakingmath]

Thanks, I'm glad you liked it! :D

[@Uchechukwu777]

Thank You tutor.

[@Justmetmt24]

Hello Miss King. I LOVE your math videos. They help me and I enjoy listening to your voice. Unfortunately, not everyone gets to hear you speak; those with hearing-loss depend on the captioning that you provide in your videos. I wanted to let you know that your closed captioning is not 100% accurate (no one's is) and as a result of this, the hearing-impaired could find such a helpful video confusing. Please check back through your captioning and fix the errors. For example at 3:04 it should say, "We multiply our result by lambda." Thank you =)

[@kristakingmath]

You're right! :) I need to do a much better job with captioning. All my new videos get captions, but working through all the old ones is a big process.

[@Justmetmt24]

It sure is. But luckily, you speak clearly and have many less errors than average. It can help to use the x2 speed option to scan through your videos quickly.

[@needlermasta]

Nice, this exact problem is in my textbook

[@CAPTMITZZYOUNG]

hey, can you please give me some questions regarding this, please.

[@notSavant]

Why is there no need for the second derivative test?

[@saradomin89898]

i believe that's just for the closed set method.

[@issayahya9051]

If it is valued, x smaller than zero gone maximum while greater than zero minimum Perhaps there were problems in the last step

[@TheBlackbeltGorilla]

Very nice video!

[@kristakingmath]

+TheBlackbeltGorilla Thanks!

[@MayankKumar-uy2iw]

Thanks mam it was really good explanation

[@claudiamendoza4620]

My finals grades thanks you

[@rakchhyapoudel4869]

Thank you so much!

[@josephblattert6311]

You are awesome and soooo helpful

[@kristakingmath]

Aw thanks!

[@johnr4906]

Great job

[@QuimicaUem]

ooooh thank you so much for share yours knowlodge it is super i cant believe

[@chidinmaadogu8242]

Great video. Would be nice if you'd respond to people's questions/input though.

[@tygao9372]

Thank you!

[@kristakingmath]

You're welcome!

[@legrosalo]

Thank you

[@kristakingmath]

You're welcome!

[@yashdggjs]

I love you

[@marie8788]

I cant thank you enough!

[@kristakingmath]

:D

[@zezusa1319]

oh god i hope i can make it

[@aliamirallana]

Thank you :)

[@farnoodlotfali4912]

not bad

[@jerryshaw8687]

x^2 = y^2 = z^2 implies that x = +- (y^2 - z^2)^1/2

[@jerryshaw8687]

+jerry shaw you didnt consider all of the possibilities

[@rivalo5]

This is not how it works. You can't just subtract 'z^2' only from 'y^2'.

[@karimhasebou4252]

my brain hurts

[@karimhasebou4252]

+Karim Hasebou but the explanation is great

[@carebyjay5185]

This vedio is really cool.I have maths final exam tommorow and so happy to find your channel.Now I am done with entire calculus which i could do in an entire year.Thank you calculusexpert.com

[@kristakingmath]

+Jayannth guduru You're welcome, I'm so glad it helped! Good luck on your final tomorrow, I hope it goes great!

[@ericzhang4464]

I like your voice!

[@ThePurdue]

LaGrONge*

[@danielgates7559]

why don't we just use the RMS-GM inequality for this question... RMS-GM is way faster at solving the problem.

[@Suppboio]

I fucked up! For the 2nd time! Nice video tho

[@hagasrama10]

thanks you beautifull you save me... :)

[@QuimicaUem]

if it was possible i could put a thousand ,million trillion like because Lagrange whit her it is so simple you SHOULD RECEIVE A NOBEL....KKKKKK

[@jimmyhaotran123]

anyone that has been hitting the gym and diet, and saw 10 cal max, and 10 cal min like me :D

[@FlyingRaptor123]

Just got an A on my test! Thank you for your vids!!

[@KarenWasherGrudzien]

HOW DO I DO THIS?

[@KarenWasherGrudzien]

MY GRAND SON HE IS 17 I DONT KNOW THIS I DROPPED OUT OF MIDDLE SCHOOL IN RURAL KANSAS TO HELP MY FAMILY WITH LIVESTOCK, FARM ETC. SO I DONT KNOW ANY OF THIS

[@dael1438]

Thank you!

[@kristakingmath]

You're welcome, Dael! :)