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Unformatted text preview: f ( x,y,z ) = x 2 + yz5 on the sphere x 2 + y 2 + z 2 = 1. 7. Find an equation of the tangent line at P ◦ = (1 ,1 , 1) to the curve of intersection of the surfaces x 2 + y 2 = 2 and y 2 + z 2 = 2. 8. Use Lagrange multipliers to determine the point P ◦ on the plane 2 xy + 3 z = 5 at which f ( x,y,z ) = 4 x 2 + y 2 + 3 z 2 has a local extremum. Is the local extremum you have found an absolute extremum? 9. Find the absolute extrema of the function f ( x,y ) = xyexy on the triangular region with vertices (0 , 0) , (0 , 4) , and (4 , 0). 10. Express the number 12 as the sum of three positive integers x , y , and z such that xy 2 z 3 is a maximum. 1...
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This note was uploaded on 04/30/2010 for the course MATHEMATIC MATH 119 taught by Professor Tor during the Spring '10 term at Middle East Technical University.
 Spring '10
 Tor
 Math

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