Go Back   Physics Help Forum > Lobby > New Users

New Users New to PHF? Post up here and introduce yourself!

LinkBack Thread Tools Display Modes
Old Mar 11th 2017, 12:26 AM   #1
Junior Member
Join Date: Mar 2017
Posts: 1
Extrema of two variable function

The temperature in a rectangular plate bounded by the lines x=0, y=0, x=3 and y=5 is T=xy^2-x^2y+100. What is the maximum temperature difference between two points on the plate?
Chander is offline   Reply With Quote
Old Mar 11th 2017, 03:52 AM   #2
Senior Member
Join Date: Jul 2009
Location: Kathu
Posts: 132
Extrema of two variable function

You can take the differential with respect to X and Y to find that the extremum sit on the line y = X/2 and for the minimum and Y = 2x for the maximum. These increase with X and Y so the maximum sits on the point 5,2.5 and the minimum on the point 1.5,3

They will be 131.25 and 93.25 respectively giving a maximum temparature difference of 38.

PS. There might also be a clever way to formulate this problem as a lagrange multiplier, but I am not really sure if it is possible because of the complexity of setting the constraints to zero.
YellowPeril is offline   Reply With Quote

  Physics Help Forum > Lobby > New Users

extrema, function, variable

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
variable potential energy caffe Energy and Work 4 Jan 25th 2012 12:15 PM
Only remain one variable. SengNee Advanced Mechanics 1 Jul 25th 2009 06:56 PM
variable capacitor rkidcd Advanced Electricity and Magnetism 2 Jun 25th 2009 04:52 AM
Is this a constant or variable force? revolution2000 Kinematics and Dynamics 2 Apr 9th 2009 09:03 AM
help with variable force revolution2000 Kinematics and Dynamics 1 Mar 29th 2009 06:46 AM

Facebook Twitter Google+ RSS Feed