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Unformatted text preview: 2 at (1,2) in the direction of ~ + ~ and directional derivative 2 in the direction of ~ + 2 . What is ~ g (1 , 2)? Check your answer. 3. 20 pts. Find all critical points, local maxima, minima and saddle points of f ( x, y ) = xy-x 2-y 2-2 x-2 y + 4. 4. (a) 10 pts. Use Lagrange multipliers to nd the maxima and minima of the function f ( x, y ) = xy subject to the constraint x 2 + y 2 = 1. Find the points where maximum and minimum occur and also the maximum and minimum values of f . (b) 10 pts. Sketch level curves of f and the graph of x 2 + y 2 = 1....
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This note was uploaded on 04/28/2008 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.
- Spring '08