It has been a while and trying to brush up on LaGrange points. I want to find the highest and lowest points on the ellipse of the intersection of the cone: x^2+y^2-z^2 ;subject to the single(adsbygoogle = window.adsbygoogle || []).push({}); constraint: x+2y+3z=3 (plane).

I want to find the points and I am not concerned with the minimum and maximum yet. So far, I have done the following:

delf<x,y,z>= lambda(del)g<x,y,z>

<2x,2y.-2z>= lambda<1,2,3> whereg(x,y,z)=3

Hence, 2x=1*lambda or (2x-1*lambda)=0

2y=2*lambda or (2y-2*lambda)=0

-2z=3*lambda or (-2z-3*lambda)=0

Furthermore, lambda=2x x=lambda/2

lambda=y or y=lambda

lambda=(-2/3)*z z=(-3/2)*lambda

Solving the systems I guess would be my area of problems. or putting things together: Using the constraint as a guideline, and solving for lambda, I obtain that lambda=7/3.

And, if lambda=7/3 x=7/6

y=7/3

z=-7/2

I would say that I am at the final steps of obtaining my points for the function; however, I am confusing myself with what points are permissible. ie.: (0,0,-7/2)

(0,7/3,0)

(7/6,0,0)

See what I am getting at? I would appreciate any guidance to putting this puzzle together

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# LaGrange Multipliers

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