Extrema subject to a constraint - illustration
This picture shows the graph of the linear function f(x,y) = x + 2y of 2 variables over the domain R2. We ask for the extrema of f only on the curve C, the circle of radius 1, which is the "constraint set". The picture suggests that, at P, f achieves an absolute maximum on this set. Note that f itself, whose graph is the plane extending infinitely in all directions, does not have an extremum.
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