2. Put f(x, y) = x + 4y. (a) Draw the ellipse with equation x +...

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2. Put f(x, y) = x² + 4y. (a) Draw the ellipse with equation x² + 2y² = 8 (b) Draw the level curves of f(x, y) corresponding to the z-values -10, -8, 8 and 10 (c) Use the method of Lagrange multipliers in order to find the min- imum and the maximum of the function f(x, y) = x² + 4y on the ellipse x² + 2y² = 8 2. Put f(x, y) = x² + 4y. (a) Draw the ellipse with equation x² + 2y² = 8 (b) Draw the level curves of f(x, y) corresponding to the z-values -10, -8, 8 and 10 (c) Use the method of Lagrange multipliers in order to find the min- imum and the maximum of the function f(x, y) = x² + 4y on the ellipse x² + 2y² = 8