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I've seen Lagrange multipliers used as a powerful method for tackling inequalities and some IMO problems, and I'm aware that it's a part of calculus. I'm currently taking BC Calculus in high school, and I'm interested in learning how to use Lagrange multipliers. Can anyone tell me anything additional that I may need to know in order to fully understand and implement the technique? Are there any textbooks that would help me in my goal particularly? Any help would be appreciated. Thank you for your time beforehand.

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If you want to do it rigorously, you're going to need a bunch more math (e.g. differential geometry). If you just want to use them to solve contest problems, see… – Potato Apr 8 '13 at 1:39
MIT OCW has a few good lectures on Lagrange… – Ben Apr 8 '13 at 2:24

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