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July 10th, 2013, 11:09 AM   #1
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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:
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July 10th, 2013, 11:16 AM   #2
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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
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July 11th, 2013, 06:43 AM   #3
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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.
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