Multivariable Calculus | Lagrange multipliers

We give a description of the method of Lagrange multipliers and provide some examples -- including the arithmetic/geometric mean inequality.

[jimallysonnevado]

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?

[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 🙏🙏🙏

[mohad]

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

[Nnm]

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

[eduardohenriquerodriguesdo]

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

[Vivian-czju]

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?

[rudypieplenbosch]

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

[lucassandleris]

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?

[georgettebeulah]

This make meaning I wish to find more video. Do you have don Williams video or tape or record. Please text me