Discussion
The method of Lagrange multipliers finds the extrema of a function subject to a constraint by
Answer: A
At a constrained extremum the level curve of \( f \) touches the constraint curve, so their normals are parallel and \( \nabla f = \lambda \nabla g \). Elimination is the alternative route, workable only when the constraint can be solved explicitly, and demanding that both gradients vanish imposes far more than is needed
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