Transcription of SOLUTIONS - UCSD Mathematics
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SOLUTIONS - UCSD Mathematics
SOLUTIONSP roblem the critical points of the functionf(x,y) = 2x3 3x2y 12x2 3y2and determine their type local min/local max/saddle point. Are there any global min/max?Solution:Partial derivativesfx= 6x2 6xy 24x,fy= 3x2 find the critical points, we solvefx= 0 = x2 xy 4x= 0 = x(x y 4) = 0 = x= 0orx y 4 = 0fy= 0 = x2+ 2y= 0we findy= 0from the second equation. In the second case, we solve the systembelow by substitutionx y 4 = 0,x2+ 2y= 0 = x2+ 2x 8 = 0= x= 2orx= 4 = y= 2ory= three critical points are(0,0),(2, 2),( 4, 8).
SOLUTIONS Problem 1. Find the critical points of the function f(x;y) = 2x3 3x2y 12x2 3y2 and determine their type i.e. local min/local max/saddle point. Are there any global min/max?
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