Ian C.

asked • 10/21/20

please help me with calculus 3 question

My professor wasn't helpful in helping me as I got the wrong answer except for one. please help me. the question is below:


Find the absolute extrema of the given function on the indicated closed and bounded set R. (Order your answers from smallest to largest x, then from smallest to largest y.


(x, y, z) = (-2, 2, 8) incorrect

(x, y, z) = (-3, -3, 108) correct

(x, y, z) = (-2squareroot3, -27, -12squareroot3) incorrect

Ian C.

the equation is f(x, y) = x3 − 6xy − y3 on R = {(x, y): −3 ≤ x ≤ 3, −3 ≤ y ≤ 3}
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10/21/20

1 Expert Answer

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Daniel B. answered • 10/22/20

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I believe there is a typo somewhere, because f(-3, -3) = -54, not 108.

The correct answer (assuming the typo is not in the statement of the problem) is (3, -3, 108).

The answer (-2, 2, 8) is incorrect because it is only a LOCAL extremum, not an ABSOLUTE one.

The answer (-2squareroot3, -27, -12squareroot3) is incorrect because it is outside of R.

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