May 11th, 2014, 02:50 AM  #1 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32  critical points of function
hi all, for function; f(x,y)= ln(x+y) + x^2  y  64 I'm trying to find all critical points & determine whether there is a local max, local min, saddle point or none of these at each critical point. thanks 
May 11th, 2014, 08:11 AM  #2 
Senior Member Joined: Dec 2013 From: some subspace Posts: 212 Thanks: 72 Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics 
Critical points are points where all the (partial)derivatives are equal to 0, and points where at least one of the derivatives is not defined. The discriminant, to determine whether the point is maxima, minima or saddle point, is: $\displaystyle \Delta = f_{xx}\,f_{yy}  f_{xy}^2$. At which part of this you have difficulties? 

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