3Blue1Brown is great

I only found this video. Could you share link of whole series/Playlist please

They dont want you to know ..

Sc Aggarwal

Good voice recognition system you got, I didn't make that connection at first but I think you are right.

His visuals say it too!

Alley00Cat Khan repeats when he writes.

And less confusing

You think it is. I prefer the books tho. I use these video's as an extra way of checking my knowledge about a certain subject.

You can make inequality into equality by introducing a variable called fictitious variable. Like x + y < 10 can be converted to x + y + w = 10, here w is fictitious variable.

I believe the most common context this is used in is economics, where resources cannot be negative, so youre probably right that there is 6 technically but for pragmatics hes just focused on the positive values

This problem contains an implied (hidden) constraint that isn’t addressed in the video. Attending to this constraint will get you the other two optimization points. If you look at the original constraint x^2+y^2=1, that implies that 1 - y^2 >=0. So all the optimization point have to fall in that region. All the points found in the video do. But we also need to check the boundary of that region, y^2=1, or y= +/-1. Putting into the original f(x,y) equation and optimizing that will give you the two other optimization points that are missing in this video.

Finally a comment that is less than a year old!

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Thanks!

You can also check the program on khan academy where, besides the lecture videos, they have lots of exercises: www.khanacademy.org/math/multivariable-calculus

only in these specific example the father u go from (0,0) the higher the function value is, what about other functions?

The max value is achieved when the contour lines touch because the question is essentially asking you to find the greatest value for x^2y such that it is within the constraints. The highest value will be where the two graphs are tangent to one another because any greater would mean they're not intersecting and thus the function would not be within the constraint.

if they arent tangent but meet, then they intersect twice (if you assume that the lines are smooth enough (if that was what you worried about you were right, there are some conditions on the functions for Lagrange multipliers to work)) and if you move now the line so that it intersect not twice but only once you get a bigger (or smaller, depending on the direction you move) value, ie the original one was not the one you were looking for

Just pour water into the 3D view, and it becomes obvious.

Hey SeungJun, not quite sure I understand your question. Do you mean you want to know how lagrange multipliers are different when you're working with transcendental functions as opposed to polynomials?

I think he used same codes like his channel (3Blue1Brown). He wrote some python codes for that.

It kinda looks like the grapher app that comes on macs.

What about how he writes so smoothly on the screen...? Boy, there are plenty of people that want to write like this!

That was just a projection of the intersection of the unit circle (cylinder) on the 3d graph of the x^2y formel.

He has a YT channel called 3blue1brown

n1er dude thank you!

Yazan Multivariable

justkarl it’s because the example here is very simple, almost trivial in a sense. Many expressions don’t have closed form solutions, and direct substitution is often very hard due to domain constraints, etc. Indeed, complex methods don’t make sense for this particular problem, but it lays groundwork for understanding more complex problems.