nt7 - f ( x, y ) = x 2-4 xy + y 3 + 4 y. Show your work....

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MATH 23 Homework 7 due March 19, 2010 Non-Text Problems: 7-1. Find the directional derivative of the function f ( x, y ) = sin(2 x - y ) at the point P ( - π 3 , π 6 ) , in the direction of the vector ± v = < π 3 , - π 6 > . Also find the direction in which f increases most rapidly at P and the maximum rate of increase. 7-2. Find equations for the tangent plane and the normal line to the surface xy + 2 yz - xz 2 + 10 = 0 at the point ( - 5 , 5 , 1) . 7-3. Find the local maximum and minimum values and saddle points of the function
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Unformatted text preview: f ( x, y ) = x 2-4 xy + y 3 + 4 y. Show your work. 7-4. Use Lagrange multipliers to find the maximum and minimum values of the function f ( x, y ) = xy subject to the constraint 9 x 2 + y 2 = 4 . Show your work. Text Problems to turn in: Friday, March 19: 14.6: 6, 16, 21; 14.7: 6, 10, 11; 14.8: 3, 4; 15.1: 4a. Text assignments for the remainder of the semester (main and complete) will be available shortly....
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This note was uploaded on 03/26/2010 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .

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