Lagrange Multipliers

This calculus 3 video tutorial provides a basic introduction into lagrange multipliers. It explains how to find the maximum and minimum values of a function with 1 constraint and with 2 constraints.
Lines & Planes - Intersection: • How To Find The Point ...
Angle Between Two Planes:
• How To Find The Angle ...
Distance Between Point and Plane:
• How To Find The Distan...
Chain Rule - Partial Derivatives:
• Chain Rule With Partia...
Implicit Partial Differentiation:
• Implicit Differentiati...
________________________________
Directional Derivatives:
• How To Find The Direct...
Limits of Multivariable Functions:
• Limits of Multivariabl...
Double Integrals:
• Double Integrals
Local Extrema & Critical Points:
• Local Extrema, Critica...
Absolute Extrema - Max & Min:
• Absolute Maximum and M...
________________________________
Lagrange Multipliers:
• Lagrange Multipliers
Triple Integrals:
• Triple Integrals - Cal...
2nd Order - Differential Equations:
• Second Order Linear Di...
Undetermined Coefficients:
• Method of Undetermined...
Variation of Parameters:
• Variation of Parameter...
________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

[@A3tutor]

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Harjot Bhui perhaps I would in class, but that‘s a different setting then. I am convinced that Indians overuse that word and I don‘t seem to be the only one.

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Fakhri yeah I agree with you, I myself don’t do that outside of class. I guess they just have a really strong habit, or maybe since this is a foreign channel to them they want to extend their respect. These are just my assumptions.

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[@stevenlitvintchouk3131]

This is the most straightforward video I've seen on how to apply Lagrange multipliers. Just what I wanted: get right to the point without the theoretical math.

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I had a test on this... _YESTERDAY._ 😭

[@Zombiecure13]

I had a test last month on this and bombed a 12 point question about Lagrange multipliers lol. I'm in vector fields right now. I'm hoping he starts uploading quicker to catch up with my class

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@@brandontruong3110 Takes too long. Three hour lectures are hard to watch when you only have 7 hours left in a day after classes.

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This video is really helpful. Now I fully understand the Lagrange multipliers!

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for using the method of Lagrange Multipliers to find Maximum and Minimum values of a function with one and two constraints. Lagrange Multipliers has many applications in Economics. Lagrange Multipliers requires solving systems of nonlinear equations. This requires some tricky algebraic manipulation. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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[@peppermint5916]

Good video. However, important to note that you can’t check if the point is minimum/maximum just by plugging in another value satisfying the condition and comparing it to the value at critical point. This is because minimum or maximum you find is LOCAL, so plugging other values is not enough. For example, think of the graph y=x^3-x^2. Its critical point is at 2/3, and it is local minimum. However, if you plug -1, you get even smaller value.

[@LuckyCrab_]

Exactly what I thought. So how do you check if it's max or min?

[@peppermint5916]

@@LuckyCrab_ there are sufficient conditions for both maximum and minimum values :) For maximum, derivative at point must be zero AND second derivative must be negative. For minimum, derivative at point must be zero AND second derivative must be positive. By second derivative I mean taking first derivative (that returns a vector of functions), and differentiating each function once more. It will result in a matrix and then you should plug in point you want to check. After that, you need to check if the matrix is positively defined, or negatively defined.

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Thank you, thank you, thank you so much for making this video. This really help a lot. you explain things better than my calc prof. I was having a terrible time understanding how to solve systems of eqs, but after watching this video, I feel confident about it. I can't thank you enough, man! Thanks!!!

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[@dominicgranada8528]

at the first example, how would you know that it is a min or max and how to find the other points?

[@sebastienalexandre4981]

I have the same question

[@kapjoteh]

You choose any 2 values for x and y and then solve for z. There’s your point.

[@someone4860]

@@kapjoteh he can also flip the value:)

[@owenyin3316]

way late, but you can also check the derivatives/second derivatives at that location and around it, I think

[@misterrandompro6181]

@@owenyin3316 huh?😬

[@nicholasalonso9477]

You explain it in such an understanding way, thank you. I would love to see more Lagrange videos

[@abdullahfarooq426]

Hi sir. In the first example, how do we know whether it is a minimum or maximum?

[@ergar90]

@Immanuel He compared it to another point that also fit the restrictions.

[@jacobguerreso675]

@@ergar90 …but is it not possible for such value to represent a saddle point? According to the second derivative test, it in fact should hold that at point (2,4,8), f attains a saddle points (Hessian matrix has determinant less than zero).

[@roxas4587]

@@jacobguerreso675 the determinate is 8 tho? fxx is 6 & fyy is 2 fxy is 0 6×2=8

[@jacobguerreso675]

@@roxas4587 the Hessian matrix would be the gradient times it’s transpose… at least, I believe so? Meaning that in this instance, the Hessian would just be a diagonal matrix of inputs 6, 2, -4 => determinant = -48

[@jacobguerreso675]

@@roxas4587 and of course, it’s also possible to check whether we have a max/min via definition using R3 balls/R2 circles/R1 intervals (by definition, if for all positive real radii “r” there exists a point greater AND a point less than f(a) in the ball/interval thing of radius “r” around point a, then we have a saddle point at point a given “a” is a critical point).

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[@atakankara6882]

How do we know that point (2,4,8) is min ? at 05:56

[@chelsea342]

Plug in another point and see if it's higher or lower than (2,4,8)

[@ErenMC_]

@@chelsea342 how do we know which point to put, as it should satisfy the constraint. Is there no other way other than trial and error?

[@anahitasingh6954]

how do you know which points fit in the constraints other than the one that you calculated (2,4,8)?

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^

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[@wrjazziel]

Thank you man for explaining Lagrange function too!

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[@GRANT-sagae]

When determining if points are at a minimum or maximum, a set of figures can be chosen based on trend analysis. I want to know how it's done

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You deserve a like. Thank you.

[@XenosKenosis]

Ist there anyway to test if lambda is minimum or max without guessing or inputing a random number that equal to the constant, it feels like it's going to take time if you're on an exam and trying random numbers idk these might be a dumb question tho

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Thank you very much for this. I have one big question though: WHY does this work? Seems like magic.

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[@apb8813]

At the extreme values, the constraining function g(x,y,z)=k and f(x,y,z) share a tangent plane to their level surfaces. What we're really doing, therefore, is saying that they share the same unit normal (gradient) vectors at that point. So grad(f)=lambda*grad(g)

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[@tylergerben3018]

Can someone tell me where he got 4,-3,7 from at 7:15

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My professor keeps taking points off my test because I'm using different methods. I don't really care tho, I'm actually learning with you😂😂

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Your teacher is a bitch. Wtf lol. You should be able to use whatever method you want. This is stupid. You should complain to his higher ups or something

[@Gqtor]

lol happened with my algebra 1 teacher. he gave me an F on a test for using derivatives to calculate the max/mins of parabolas instead of the -b/2a sh*t even though I got everything right. dropped his class and got a perfect score on the EOC. needless to say some teachers are annoying for zero reason if your method works, use it, but hopefully u got a good grade nonetheless 😥

[@KR-kk9fh]

@@Gqtor well duh you're taking algebra 1 and using calculus on your test. I would have taken points off as well. He is testing your algebra skills not calculus.

[@Gqtor]

@@KR-kk9fh i mean im in college now, but i disagree with that opinion. if you have a method to solve a problem, you should be able to use it. the real world isn't "hey find the peak of this parabola using ONLY algebra" it's just "find the peak of this parabola i don't care how you get it just put it on my desk in 10 minutes".

[@t_mm_r]

@@Gqtor the problem is, you should know why the method you use works. Have you proved the formula of a derivative of a parabola and the necessity and the sufficiency of an extremum?

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God I had to learn this thing in an hour!! Thanks so much

[@fayyazhussain2963]

Thanks for clearing my point

[@user-jl6mn5dz4e]

Is it just a random point or is there reasoning for the second and third point examples he puts

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the savior of all math students lol

[@ErenMC_]

When we are checking whether the given point is minima or maxima, how do we know the points which fit the constraint to compare whether it is minima or maxima? (like how did you think of (4,-3,7) in the first question)

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I’m literally sitting in calc 3 watching this on mute bc it’s more helpful than my professor in half the time

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Well explained keep it up sir 💪

[@samueldeklerk4573]

What about lambda equals zero for 3

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son örnek çok güzeldi. last example was really good.

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this is beautiful

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I have an exam today and this is very hel

[@mathiaswakgari8255]

What about a triangle Constraint

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Thank you!

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Thanks for the great tutorial

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[@Aaron-bl2tj]

Great video, thanks!

[@xarran]

In question 1. you were asked to find minimum and maximum but you only found minimum... so how do I find maximum in the first example? 🧐

[@joshuazhou1239]

Not finding both maximum and minimum, you are finding any max or min, so in this case, that point was a minimum value.

[@jacobguerreso675]

In the case you were looking for the max, in this problem since there exists only one critical point (which was associated with a min), it must hold then that unless that critical point reps a max value (which it doesn’t), then there exists no maximum and thus no upper bound (unbounded map f… which I assume holds here).

[@Sting_raider]

how would you find the max value for the first question?

[@dontshout2177]

please do Laplace theorem both 2D and 3D

[@shaatiusmani6211]

thank you ❤

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You're awesome man !!!

[@sum1sw]

That's a great explanation. Thank you for posting. Do you have a video on how to apply L.M. to a non-linear regression problem with constrains,when I have initial guesses for my variables X, Y, Z. I can calculate the derivatives and the constraints numerically. and, of course, there is no way on Earth, the partial derivatives with respect to each adjustable parameter will give me the same Lamda in all equations. how would one iterate and adjust the initial guesses of the adjustable parameters to satisfy the equations?

[@nasseromar6309]

Question: The values you are using to show if its a local min or max, where do you get these numbers from, are they just pulled from thin air???

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[@theeyepatche7080]

Hi man

[@theeyepatche7080]

Do you have exam can you send me so of you exercises

[@danielmoore5796]

Great video.

[@biggod0015]

Sir In your third question ; Given f(x,y,z)=4x+2y+6z and x²+y²+z²=14. Use Lagrange multipliers to find any maximum or minimum value. In your calculations, after finding (x,y,z), you substituted it in x²+y²+z²=14 . Right. Sir I finished calculating it and equate it 14 ie(11/lander²=14) Sir isn't there a mistake there🙋

[@kwizerasept7983]

thanks so much Tutor much repect to you

[@aloksharma4611]

Thanks!

[@ZombieChicken-X]

how are you finding other points that fit the constraint