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?
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 🙏🙏🙏
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.
Love the AM GM example
Love the explanation
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?
I wish this included a proof or at least some sort of explanation on why this method magically works
Very nice result 👌🏾
how do we know that it's the absolute maxima and not minima?
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 🙏🙏🙏
Thanks for showing an excellent example of multi variable calculus. Steve Brunton showed basics, but he did not show a good example.
but how do you prove that a critical point is not a saddle?
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.
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?
thats what Im saying, wouldnt lambda be 1 if we solved for lambda using that?
If Lambda is 1, y is 0. And that means x = +/- 1. Which has already been addressed.
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?
I am wondering where the n*x_1 comes from when doing the derivative.
@@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
he a gangster
This make meaning I wish to find more video. Do you have don Williams video or tape or record. Please text me