Finding Maxima, Minima, and Saddle Points with Lagrange Multipliers

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The discussion focuses on the challenges of determining whether points found using Lagrange multipliers are maxima, minima, or saddle points. The user expresses difficulty in finding clear methods in literature, mentioning the Bordered Hessian as a potential approach but noting its vague explanations. They seek assistance or resources that provide a clearer understanding of the criteria for classifying these points. A response indicates that the provided information was helpful. Clear guidance on this topic is essential for effective optimization.
ythamsten
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I'm currently having some trouble, after the procedure of finding the actual values for the multipliers and the points, but how come can I figure out whether which points that I've collected are maxima, minima or just saddle ones. I've taken a look on lots of books, but I can't seem to find something that helps me out with a method that I can apply in general. The closest I reached of something useful was called the 'Bordered Hessian', which was fairly similar to usual optimization, but where I was reading, the criteria was described in kind of a fuzzy way. Can someone help me? Or at least indicate where I can find this in a clear way? Thanks!
 
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This should help you
 
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It surely did zoki85! Thanks a lot.
 

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