July 10th, 2013, 11:09 AM  #1 
Newbie Joined: May 2012 Posts: 17 Thanks: 0  Multivariable maxima and minima
Hi! I'm having trouble finding maxima and minima for functions of more than one variable, with constraints, especially when the constraint is an inequality. For example: 
July 10th, 2013, 11:16 AM  #2 
Newbie Joined: May 2012 Posts: 17 Thanks: 0  Re: Multivariable maxima and minima
Sorry, I clicked submit by accident: with , , I derived F with respect to x and y, and searched for critical points, which gave me x=0 and y=0, and this point is not in the specified domain. I tried using Lagrange's multipliers but I get a system of three equations, two of which are the same, so I can do nothing! Help me! I'm desperate!!! hahaa 
July 11th, 2013, 06:43 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Multivariable maxima and minima
"Lagrange multipliers" does not apply to this. The fact that the partial derivatives are not 0 in the given region means there are no max or min inside the region so you need to look on the boundaries. If x= 1, if y= 1, if , Look for max and min on each of those intervals. You will also want to find the points where those connect to find the "boundaries" of the boundaries. 

Tags 
maxima, minima, multivariable 
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