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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,

    e^-(x^(2)+y^(2)+2x)

    2. Relevant equations

    none

    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

    and

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

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

    thanks,
    Dan
     
  2. jcsd
  3. Jan 22, 2012 #2

    Dick

    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.
     
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