final-practice-sol1 - Math 10C Fall 2009 Final Exam Problem...

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Math 10C - Fall 2009 - Final ExamProblem 1.[15 points]At what point(x, y, z)on the planex+ 2y-z= 5does the minimum of the functionf(x, y, z) =x2+ 2y2+ (z+ 1)2occur?
Problem 2.[20 points.]Consider the functionf(x, y) = 3y2-2y3-3x2+ 6xy.(i)[8] Find the critical points of the function.(ii)[8] Determine the nature of the critical points (local min/local max/saddle).(iii)[4] Does the functionf(x, y)have a global minimum or a global maximum?Answer:
Problem 3.[13 points]Consider the functionf(x, y) = ln(xy2)-2xy(i)[8] Compute the second order Taylor polynomial offaround(1,1).(ii)[5] Find the tangent plane to the graph offat the point(1,1,-2).Answer:

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