Lagrange Multipliers PART 2/2 (KristaKingMath)

Lagrange Multipliers calculus example.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[kristakingmath]

Ya some of my early videos I was still trying to get the hang of everything, and the um's were a definitely a bad habit. Hopefully my newer videos are a little better! :)

[justingutierrez]

Afterstruggling for over an hour for having somebody explain to me how to find the max or min in a lagrangian, you managed to answer that in less than 5! Thank you so much :D

[nicolereplogle]

Re: 5:50) If the discriminant is greater than zero, it means that the second order derivatives for X and Y *both* have the same sign (both positive or both negative, so that multiplied together they come out positive). So you actually *can* evaluate the second order derivative for Y if that winds up being easier, since they'll both either be greater than zero, or both less than zero. Thanks for the wonderful video, I like your method more than my prof's :) Edit: I meant "discriminant" not "determinant". Woops!

[collinsbarasa]

highly appreciated work miss.Be abundantly blessed;your work is helping millions of students globally.

[kristakingmath]

@erlarson8 I looked for a video on second order partial derivatives, and COULD NOT believe I didn't have one! So I just filmed one, and I'll be posting it up tomorrow! :D

[kalvin]

+Gerardo Lopez it is called the Second Partials Test. It tells you whether or not your point is a relative min, relative max, a saddle point, or inconclusive test.

[elpbm]

Excellent Video. Is there a video which explains more about what a lagrange multiplier is.

[gnarasim]

Krista you are so awesome at teaching me lagrange !!! love u :) Thanks for all the help u gave me, now i can ace my test .

[nathanturner]

A saddle point is a maximum and a minimum depending on the orientation. The middle of a pringle is a maximum lengthways and a minimum crossways. Gets the name from the fact that saddles share this shape.

[shannonjackson]

I took calculus 3 in high school and found it to be easy.. little did I know I only knew the basics. When I took it in college at Maryland I was shocked that I got a D... now after watching your videos I actually understand it so hopefully I'll pull my grade up to a B now!

[giovannifoulmouth]

but 2x+6y=2000 is a line in the xy plane, so u could just take any point on this line infinitely far away from the origin and our function will be defined there which means the function doesn't have a maximum on the line it has just a minimum at some point, right ?

[kristakingmath]

Awww! Well I'm glad you like it; I'd love to be your teacher as much as I can, just here on YouTube! :)

[guitarttimman]

A local minimum given the constraint. I think it would be a slanted plane that intercepts the elliptical paraboloid on the lower slant at the point g(100, 300). That would be the steepest ascent of the plane going up. Okay.

[jkrupa]

If the discriminant, D(x, y, lambda) is positive, the easiest way to know if it is a local max or a min is by thinking of the second partial Dxx or Dyy. If one of these is negative, then your function is concave down, so you are at a max (concave down looks like a frown). The same can be said for the case where Dxx or Dyy is positive, when it is a min. 

[PigeonTendies]

I've seen different examples of Lagrange Min and Max problems, but I don't know exactly what prompted you to use the D(x, y, lambda) equation 

[erlarson]

Thanks for the videos they are perfect! have you made videos for 2nd order partial derivatives? Thanks again!

[johnames]

Thanks for the excellent videos. Wish people would stop leaving such creepy comments, bless 'em. Anyway, good work and glad to see you are still continuing :)

[HAL]

Useful lesson, but I am confused, what should I do when the second partial derivatives all equal zero? How do I find the maximum and minimum?

[eolayo]

I love watching your videos because you do it slowly and explain everything. But for this video part one and two it seemed you werent as confident, you said um so many times lol.... still loveee uuuu much love from LA =)

[scalesconfrey]

That version is when you are trying to optimize globally, this version uses constraints, so it is automatically the point.