1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Critical points multivariable

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Locate the critical point of the function,


    2. Relevant equations


    3. The attempt at a solution
    Ok first step differentiate the function and set it to zero for both fx and fy,

    Fx(x,y) = (-2x-2)e^(-x^(2)-y^(2)-2x)
    Fy = -2ye^(-x^(2)-y^(2)-2x)

    Now I need to solve both equations simultaneously,

    I get

    ln(-2x-2)-x^(2)-y^(2)-2x = 0


    ln(-2y)-x^(2)-y^(2)-2x = 0

    and this is where I am stuck. :( any advice would be welcomed :D

  2. jcsd
  3. Jan 22, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    You need to solve Fx(x,y)=0. You don't want to take the log of that. log(0) is undefined, it's NOT 0. The way to do this is to notice e^a is NEVER 0. So e^(-x^(2)-y^(2)-2x) is NEVER 0. The only way Fx(x,y) could be 0 is if (2x-2) is 0.
  4. Jan 22, 2012 #3
    ah thank you.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook