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Given a function $g(x,y,z)$ we need to maximize it given constraints $a.

If the constraints were given as a function $f(x,y,z)$ the following equation could be used.

$\nabla f(x,y,z) = \lambda \nabla g(x,y,z)$

How would I set up the initial equation given an interval constraint. Or how would I turn the interval constraint into a function constraint.

EDIT:: Added $a to the constraints.

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    Hint: consider a function such as $(x-(a+b)/2)^2$2012-11-10

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