Final answer:
To find the absolute maximum and minimum values of the function f(x, y), we need to clarify the function's expression due to a possible typo and consider the critical points and the behavior on the boundary of the domain.
Step-by-step explanation:
The student has asked to find the absolute maximum and minimum values of the given function f(x, y) = x² * y² * x²y + 8 over the specified domain d, which includes all points (x, y) such that -1 ≤ x ≤ 1 and -1 ≤ y ≤ 1. To find these values, one needs to analyze the critical points within the domain as well as the function's behavior on the boundary of d.
The critical points can be found by setting the partial derivatives of f with respect to both x and y to zero and solving for x and y. However, due to the domain restrictions and the nature of the function, which appears to have a typo in the given expression, a clarification would be needed before proceeding with a solution. If the function was correctly stated, we would indeed calculate the partial derivatives, set them to zero, and solve for potential critical points within the domain. Additionally, we would evaluate the function along the boundaries where either x or y is equal to -1 or 1 to ensure we have considered all possible maximum and minimum values.
Ultimately, the actual values for the maxima and minima would depend on the corrected form of the function f(x, y).