My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
July 10th, 2013, 11:09 AM   #1
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:
chrishaig is offline  
July 10th, 2013, 11:16 AM   #2
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
chrishaig is offline  
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.
HallsofIvy is offline  

  My Math Forum > College Math Forum > Calculus

maxima, minima, multivariable

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
maxima minima (2) helloprajna Calculus 3 October 13th, 2012 04:03 AM
maxima and minima kingkos Calculus 3 April 10th, 2012 08:20 AM
maxima minima bhuvi Calculus 1 September 5th, 2010 05:35 AM
Maxima or minima ArmiAldi Real Analysis 1 March 6th, 2008 04:51 AM
maxima minima bhuvi Algebra 1 December 31st, 1969 04:00 PM

Copyright © 2019 My Math Forum. All rights reserved.