Question

Use Lagrange Multipliers to find the absolute maximum and minimum of f(x,y)=3x² +y² on the curve described by xy=1 between x=1/2 and x=2.

Answer 1

To find the absolute maximum and minimum of f(x,y)=3x² +y² on the curve described by xy=1 between x=1/2 and x=2, you can use the method of Lagrange Multipliers. Here are the steps: Set up the system of equations, take the partial derivatives, solve the system of equations, plug the critical points into f(x,y), and find the maximum and minimum values of f(x,y).

Step-by-step explanation:

To find the absolute maximum and minimum of the function f(x,y) = 3x² + y² on the curve xy = 1 between x = 1/2 and x = 2, we can use the method of Lagrange Multipliers. Here are the steps:

1. Set up the system of equations:
2. Take the partial derivatives of f, g, and λ(g(x, y) - c) with respect to x, y, and λ respectively, and set them equal to zero.
3. Solve the system of equations to find the critical points.
4. Plug the critical points into f(x, y) to find the values of f(x, y) at those points.
5. Find the maximum and minimum values of f(x, y) from the values obtained in step 4.

By following these steps, you can find the absolute maximum and minimum of the function on the given curve.