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Unformatted text preview: x 2 +9 y 2 +4 z 2 = 9, where the edges of the box are assumed to be parallel to the coordinate axes. (You can assume that a box of maximum volume exists.) 5. Suppose that for some dierentiable function f ( x, y, z ) we know that the maximum value of the directional derivatives D u at the point (1 , 1 , 1) is 2, and this maximum occurs in the direction of the vector (1 , 2 , 2). (8 pts) (a) From this information, compute f (1 , 1 , 1). (7 pts) (b) Compute D u (1 , 1 , 1) in the directions of the vectors (2 , 1 , 2) and (1 , 1 , 0). (15 pts) 6. Suppose that a dierentiable function f ( x, y ) has f x (5 , 3) = 4 and f y (5 , 3) = 6. Suppose also that x and y are related to variables u and v by x = u 2 + v 2 and y = u 2 v 2 . Compute f u and f v at ( u, v ) = (2 , 1)....
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This note was uploaded on 04/19/2010 for the course MATH 2220 taught by Professor Parkinson during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 PARKINSON
 Math, Multivariable Calculus

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