Final answer:
To find the absolute maximum value of the function f(x, y) = x² - y² on the curve x ≥ y², x ≤ 4, we can graph the function and evaluate it at the critical points and endpoints.
Step-by-step explanation:
To find the absolute maximum value of the function f(x, y) = x² - y² on the curve x ≥ y², x ≤ 4, we can first graph the function and identify any critical points and endpoints within the given range. By completing the square, we can simplify the condition to 2(x² - ¹)² ≤ 4. It is important to note that the graph will be a declining curve. To find the maximum value, we evaluate the function at the identified critical points and endpoints to determine the absolute maximum.