Final answer:
To find the maximum and minimum of f(x,y,z) = 2x+y - z subject to the constraints 2x + z = 2/√5 and x²+y²/4 = 1, we can use Lagrange multipliers.
Step-by-step explanation:
To find the maximum and minimum of the function f(x, y, z) = 2x + y - z subject to the constraints 2x + z = 2/√5 and x² + y²/4 = 1, we can use Lagrange multipliers. First, we set up the Lagrangian function L(x, y, z, λ₁, λ₂) = 2x + y - z + λ₁(2x + z - 2/√5) + λ₂(x² + y²/4 - 1). We then take the partial derivatives with respect to x, y, z, λ₁, and λ₂ and set them equal to zero. Solving these equations will give us the critical points, which we can analyze to determine the maximum and minimum values of the function.