Question

Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra system to confirm your results. (There are multiple correct answers.) f(x, y) = 2xy/(ˣ² + 1)ˣ² + 1) R = {(x, y): 0 lessthanorequalto x lessthanorequalto 1, 0 lessthanorequalto y lessthanorequalto 1} absolute maximum (x, y, z) = (0, 1, 4) absolute minimum (x, y, z) = (1, 1, 0)

Answer 1

To find the absolute extrema of a function over a given region, we evaluate the function at the boundary points and critical points inside the region.

Step-by-step explanation:

The problem asks us to find the absolute extrema of the given function f(x, y) = 2xy/(x² + 1)² over the region R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}. To find the absolute extrema, we need to evaluate the function at the boundary points and critical points inside the region. The given absolute maximum is (0, 1, 4) and the absolute minimum is (1, 1, 0).