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Solutions to Exam 1 - Johns Hopkins University
www.math.jhu.eduSolutions to Exam 1 1. Let f(x;y) = x2 +y2 +xy ¡x+y: (a) Show that x = 1;y = ¡1 is the only critical point of f. Solution: To find the critical point, set fx = 0 and fy = 0 to obtain the equations 2x+y ¡1 = 0;2y +x+1 = 0 which has the solution x = 1;y = ¡1. (b) Use the second derivative test to show that x = 1;y = ¡1 is a local mini- mum (and thus an absolute minimum it is the only ...