My Math Forum Multivariable maxima and minima

 Calculus Calculus Math Forum

 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: $F(x,y)=\pi x\sqrt{x^2+y^2}, with x\ge1, y\ge1, x^2+y^2\le16$
 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: $F(x,y)=\pi x\sqrt{x^2+y^2}$ with $x\ge1$, $y\ge1$, $x^2+y^2\le16$ 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, $F(1, y)= \pi\sqrt{y^2+ 1}$ if y= 1, $F(x, 1)= \pi x\sqrt{x^2+ 1}$ if $x^2+y^2= 16$, $F(x,y)= \pi x\sqrt{16}= 4\pi x$ 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

 Thread Tools Display Modes Linear Mode

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

 Contact - Home - Forums - Cryptocurrency Forum - Top