Final answer:
The question involves finding the absolute maximum and minimum of the function f(x, y) over a given rectangular domain. This requires using partial derivatives to find critical points inside the domain and evaluating the function on the boundaries of the domain.
Step-by-step explanation:
The student is asking about finding the absolute maximum and minimum values of the function f(x, y) on a specific domain d, which is a rectangle in the xy-plane. To find these extremal values, one typically uses a combination of critical point analysis within the domain for local maxima and minima, along with an evaluation of the function on the boundary of the domain. In this case, the function's boundary is defined by 0 ≤ x ≤ 4 and 0 ≤ y ≤ 5. To start, find the partial derivatives of f with respect to x and y, set them equal to zero, and solve for x and y to find critical points. Next, evaluate f at these critical points as well as along the edges of the rectangle to locate the maxima and minima. Note that the task directly instructs to ignore the provided reference information as it seems to be irrelevant to the question asked.