Multivariable Calculus | Lagrange multipliers

[@ProfOmarMath]

Love the AM GM example

[@mathadventuress]

Love the explanation

[@jimallysonnevado3973]

In the second example, why can we be sure that it is a maximum? Can it be also be the absolute minimum since we can only be sure that it is a critical point?

[@mohad12211]

I wish this included a proof or at least some sort of explanation on why this method magically works

[@vasilisr7]

Very nice result 👌🏾

[@Nnm26]

how do we know that it's the absolute maxima and not minima?

[@ranam]

My question may be strange but I have no one to ask this can you tell me a Lagrange algorithm to find a minimum arbitrary volume within another volume which can contain it by maximum of it inside it or minimum of it out side 🙏🙏🙏

[@rudypieplenbosch6752]

Thanks for showing an excellent example of multi variable calculus. Steve Brunton showed basics, but he did not show a good example.

[@eduardohenriquerodriguesdo6103]

but how do you prove that a critical point is not a saddle?

[@MichaelPennMath]

In the first example you are guaranteed to have a max and min given that the constraint curve represents a closed and bounded region of the plane. The same is true in the second example, but I should have been a bit more careful with the setup-- xi>=0.

[@Vivian-cz7ju]

How do we know that all the solutions have been found to the set of equations? Shouldn't we also solve for the equation in x where 2x = 2xlambda?

[@suvhamdhital7126]

thats what Im saying, wouldnt lambda be 1 if we solved for lambda using that?

[@thesecondderivative8967]

If Lambda is 1, y is 0. And that means x = +/- 1. Which has already been addressed.

[@lucassandleris4486]

What happens if we try to find the min value of ⁿ√(x1.x2...xn) when x1+x2+...+xn=c ? How do Lagrange multipliers apply in that case?

[@michaelempeigne3519]

I am wondering where the n*x_1 comes from when doing the derivative.

[@Boringpenguin]

@@michaelempeigne3519 (x_1)^(-1) = 1/(x_1) So you can separate a (x_1)^(-1) from (x_1)^((1/n)-1) and put it in the denominator

[@natepolidoro4565]

he a gangster

[@georgettebeulah4427]

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