My Math Forum Local max, local min, or saddle point

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 February 27th, 2015, 02:54 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, 03:14 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 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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