Question

Find the extreme values of f on the region described by the inequality. f(x, y) = e⁽⁻ˣʸ⁾; x² - 4y² ≤ 1?

Answer 1

To find the extreme values of the function f(x, y) = e^(-xy) on the region described by the inequality x^2 - 4y^2 ≤ 1, we need to first determine the critical points and then evaluate the function at these points and on the boundary.

Step-by-step explanation:

To find the extreme values of the function f(x, y) = e^(-xy) on the region described by the inequality x^2 - 4y^2 ≤ 1, we need to first determine the critical points and then evaluate the function at these points and on the boundary.

1. Find the partial derivatives of f with respect to x and y, and solve the resulting equations to find the critical points.
2. Evaluate f at the critical points and on the boundary x^2 - 4y^2 = 1.
3. Compare the values obtained in step 2 to determine the minimum and maximum values of f.

By following these steps, you can find the extreme values of the function f(x, y) = e^(-xy) on the given region.