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Math 20C Final 7 (No Solutions)

# Math 20C Final 7 (No Solutions) - Final Exam Math 20C Dr...

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Final Exam, Math. 20C Dr. Cristian D. Popescu March 14, 2005 Name: Student ID: Section Number: Note: There are 5 problems on this exam. Each of them is worth 40 points. You will not receive credit unless you show all your work. No books, calculators, notes or tables are permitted. I. (40 points) Let f ( x, y ) be the function given by f ( x, y ) = x 4 + y 4 - 4 xy + 1 . (1) Determine the critical points of f ( x, y ). (2) Classify the critical points of f ( x, y ) into local maxima, local minima, and saddle points, respectively. (3) Determine the global maximum and minimum points of f ( x, y ) on the (closed and bounded) domain D = { ( x, y ) | 0 x 3 , 0 y 2 } . (4) Use the method of Lagrange multipliers to find minimum value of f ( x, y ) along the curve given by the equation 4 xy = 1 . Is there a maximum value for f along the given curve ?

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II. (40 points) (1) Compute the integral ZZ D f ( x, y ) dA , where f ( x, y ) = y cos( x 2 ) and D is the plane region situated above the x –axis and bounded by the curves y = 0, x = y 2 , and x = 9.
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