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 and 2nd partials test

  1. Apr 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Find all critical points of f(x,y) = 12xy-x^2 y-2xy^2 and test them for relative extrema using the 2nd partials test.

    2. Relevant equations



    3. The attempt at a solution

    {0=fx(x,y)=12-2x-2 10x-2 x=5
    {0=fy(x,y)=12-4y y=3

    Critical point: (5,3)

    fxx(x,y)= -2
    fyy(x,y)= -4
    fxy(x,y)= 0

    d(5,3)=fxx(5,3)fyy(5,3)-(fxy(5,3))^2
    d=(0)(0)-(0)
    d=0 no conclusion
    ---------------------------------------

    Just wondering if I did this right?
     
  2. jcsd
  3. Apr 3, 2009 #2

    HallsofIvy

    User Avatar
    Science Advisor

    fxx(5,3)fyy(5,3)= (-2)(-4), not (0)(0)!
     
  4. Apr 3, 2009 #3
    Ok, so

    d=(-2)(-4)-(0)
    d=8

    Is that right?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook