Calculus 3 Quiz
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MULTIVARIABLE FUNCTIONS & PARTIAL DERIVATIVES
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Consider the constrained optimization problem: minimize f(x,y)=x2+y2f(x,y) = x^2 + y^2 subject to (x−1)2+(y−1)2=2(x-1)^2 + (y-1)^2 = 2. A student sets up the Lagrangian and finds the condition 2x=2λ(x−1)2x = 2\lambda(x-1) and 2y=2λ(y−1)2y = 2\lambda(y-1). If they conclude that x=yx = y at the critical points, which additional step is necessary to find the minimum value of ff?
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