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Find the absolute maximum value of the function f(x, y) = x² - y² on the curve x ≥ y², x ≤ 4.

User AutoSponge
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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.

User Heather Claxton
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