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So the assignment is to provide an informal interpretation of Lagrange multiplier method (under 30 words and without math formulas). The main idea is to show intuition on why the method works and then state the insight in common and concise words to convince someone with sufficient math education that you understand why it works.

So far I am getting this

"Lagrange multiplier gives us normal vectors of constraint and level curves inline with each other of the extreme value with respect to the constraint".

Can someone comment if what I am saying makes sense to the assignment ?

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  • $\begingroup$ All directional derivatives of a function constrained to a surface will vanish at a point where the gradient of the function is normal to the tangent plane of the surface. $\endgroup$ – WW1 Mar 27 '17 at 5:08
  • $\begingroup$ @WW1 would that be a more appropriate interpretation ? $\endgroup$ – Rogertherabbit5 Mar 27 '17 at 5:30
  • $\begingroup$ To be frank, if you gave me the sentence but the first two words, I would not understand it and even less recognize the Lagrange multiplers. I don't even think it is grammatically sound. $\endgroup$ – Yves Daoust Mar 27 '17 at 7:09
  • $\begingroup$ @Yves Daoust sorry do you mind explaining which sentence you are referring to ? The one in my question or the one in the comment ? $\endgroup$ – Rogertherabbit5 Mar 27 '17 at 21:32
  • $\begingroup$ I was addressing you. $\endgroup$ – Yves Daoust Mar 28 '17 at 6:26
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60 words.

If the restriction of a function to an hypersurface admits a maximum at a point, then its derivative vanishes on the tangent hyperplane of the hypersurface at this point. If a linear form (the derivative of the function) vanishes on the kernel on another one (the tangent hyperplane), then they are proportional. The Lagrange multiplier is the coefficient of proportionality.

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When miniminzing a function under an equality constraint, the gradient must be orthogonal to the constraint surface, i.e. equal to the gradient of the constraint function times a multiplier.

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