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  3. (6) consider the function f(x, y) = 9 ? x^2 ? y^2

(6) Consider the function f(x, y) = 9 ? x^2 ? y^2 restricted to the domain...

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Basic Math

(6) Consider the function f(x, y) = 9 ? x^2 ? y^2 restricted tothe domain x^2/9 + y^2 ? 1. This function has a single criticalpoint at (0, 0)

(a) Using an appropriate parameterization of the boundary of thedomain, find the critical points of f(x, y) restricted to theboundary.

(b) Using the method of Lagrange Multipliers, find the criticalpoints of f(x, y) restricted to the boundary.

(c) Assuming that the critical points you found were (±3, 0) and(0, ±1, find the absolute maximum and minimum of f(x, y) restrictedto this domain.

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