a7 - xy + z 2 on the surface x 2 + y 2 + z 2 = 1. 7. Let f...

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Math 237 Assignment 7 Due: Friday, Due Mar 11th * 1. Find the absolute maximum and minimum values of f ( x,y ) = 2 x + x 2 + y 2 - xy 2 in the region bounded by the parabola 2 x + 4 = y 2 and the line x = 2. * 2. Find the points on the surface z = x 2 + y 2 that is closest to the point (1 , 1 , 0). * 3. Use the method of Lagrange multipliers to find the maximum and minimum values of f ( x,y ) = x on the piriform curve defined by y 2 + x 4 - x 3 = 0. 4. Find the maximum and minimum of f ( x,y ) = x 2 - y 2 on the region x 2 + y 2 1. 5. Find the maximum and minimum of f ( x,y ) = x 3 - 3 x + y 2 + 2 y on the region bounded by the lines x = 0, y = 0, x + y = 1. 6. Use the method of Lagrange multipliers to find the maximum and minimum values of
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Unformatted text preview: xy + z 2 on the surface x 2 + y 2 + z 2 = 1. 7. Let f ( x,y ) = x 2 + y 2-1 2 y . a) Use the method of Lagrange multipliers to nd the maximum and minimum points of f ( x,y ) on the curve y = 1-2 x 2 . b) Let R be the region bounded by the curve y = 1-2 x 2 and the x-axis. Find the maximum and minimum value of f ( x,y ) on the region R . NOTE: Only * questions will be graded...
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