ENADE Matemática Practice Questions - ENADE Matemática - Exame Nacional De Desempenho Dos Estudantes Exam

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Using the method of Lagrange multipliers, find the global maximum and minimum values of $f(x,y) = x^2 + 2y^2$ subject to the circle constraint $x^2 + y^2 = 4$.

Maximum value is 4 at $(0, \pm 2)$ and minimum value is 2 at $(\pm 2, 0)$. Maximum value is 8 at $(0, \pm 2)$ and minimum value is 4 at $(\pm 2, 0)$. Maximum value is 16 at $(\pm 2, \pm 2)$ and minimum value is 0 at $(0,0)$. Maximum value is 6 at $(\sqrt{2}, \sqrt{2})$ and minimum value is 4 at $(2,0)$.

Correct Answer:

Maximum value is 8 at $(0, \pm 2)$ and minimum value is 4 at $(\pm 2, 0)$.

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