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February 27th, 2015, 03:54 PM  #1 
Newbie Joined: Feb 2015 From: United States Posts: 2 Thanks: 0  Local max, local min, or saddle point
I have a function g(x,y) = x^2*y  x  1 for which my partial derivatives set equal to 0 are 2xy  1 = 0 and x^2 = 0. Solving the 2nd equation, I get x = 0. If I plug in 0 into the first equation, both x and y goes away because they are being multiplied by 0. What to do in this case ? I have to find critical points, and also local max, local min, or saddle point.

February 27th, 2015, 04:14 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,783 Thanks: 2197 Math Focus: Mainly analysis and algebra 
So the second equation has no solutions when $x=0$, but the first tells you that any critical points must be on $x=0$. What is the logical conclusion?


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local, max, min, point, saddle 
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