What is the maximum value of the function f(x, y) = x y subject to the constraint x^2 + y^2 = 8?
Answer and explanation
Correct answer: D. 4
- Step 1: Using AM-GM inequality: (x^2 + y^2) / 2 ≥ sqrt(x^2 * y^2) = |xy|.
- Step 2: Since x^2 + y^2 = 8, we have 8 / 2 ≥ |xy| => |xy| ≤ 4.
- Step 3: Equality occurs when x^2 = y^2 = 4 (e.g. x = 2, y = 2), giving xy = 4.
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