1. Not finding help here? Sign up for a free 30min 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!

Classifying Critical Points

  1. Mar 8, 2009 #1
    1. The problem statement, all variables and given/known data
    f(x,y)=xy+(144/x)+(12/y)
    f has a relative minimum at ( , , )

    2. Relevant equations

    Partial derivatives

    3. The attempt at a solution
    fx=y-(144/x^2)
    fy=x-(12/y^2)

    I setted these to zero. Multiplies both sides so there is no fraction.

    Came out to be something like~~~ x2y-144=0
    xy2-12=0

    then did the factoring stuff and got

    x2-12xy2=0

    This tells me that the critical point is (0,0), but this is the wrong answer.

    PLEASE TELL ME WHAT I AM DOING WRONG.

    THANK YOU SO MUCH TO THOSE WHO HELP. THIS FORUM IS HELPING ME BECOME A BETTER MATHMATICIAN AND THEREFORE, MY TEST GRADES ARE GOING UP. THANK YOU.
     
  2. jcsd
  3. Mar 8, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Your partial derivatives and general procedure are correct:smile:; but your attempt to solve for x and y is very confusing...try solving the f_y=0 equation for x, and substitute that result into your f_x=0 equation and solve for y....
     
  4. Mar 9, 2009 #3

    lanedance

    User Avatar
    Homework Helper

    just to add - there can be (and is in this case) more than one stationary point

    as you mentioned (0,0) is a stationary point, but that doesn't automatically make it an extremum - need to look at the 2nd order partial dervatievs to determine that
    Edit - (0,0) is not a critical point
     
    Last edited: Mar 9, 2009
  5. Mar 9, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    (0, 0) most certainly is NOT a stationary point- it's not even a point on the graph. f is not defined at (0,0).
    And I get only one critical point.
     
  6. Mar 9, 2009 #5

    lanedance

    User Avatar
    Homework Helper

    yeah - looked at that a little too quickly, sorry for the mis-steer
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook