Unformatted text preview: ) =-2 x 2 + 3 xy + y 2-4 x + 3 y-1. (a)(7 pts) Find all critical points of f . Specify which of these points correspond to relative maximum values, relative minimum values and saddle points of f . Hint: Apply the second partials test. (b)(3 pts) Suppose that f takes values in the region R de±ned by x 2 + y 2 ≤ 4. Explain brie²y why f has a maximum and a minimum value in R . Are such values attained in the interior or at the boundary of R ? Hint: In part (b), you may use your result from (a). Then, the answer to (b) is really short! 4. (10 pts) Consider the function w = f ( y-x, y-z, z-x ). Assume that partial derivatives of f exist. Compute the sum A = ∂w ∂x + ∂w ∂y + ∂w ∂z ....
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This note was uploaded on 04/08/2008 for the course MATH 241 taught by Professor Wolfe during the Fall '08 term at Maryland.
- Fall '08