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 point of two variable function

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Each of the functions f have a critical point at (0,0), however at this point the second derivatives are all zero. Determine te type of critical point at (0,0) in this case

    1) f(x,y)=x2y+xy2
    2)f(x,y) = x4+2*x3y+x2y2+y4

    3. The attempt at a solution

    For the first part by plotting it on Wofram I saw that it was a saddle, and i substituted the values x=y and x=-y to show that there is a saddle point in one direction and a straight line in the other, hence a saddle point, is this sufficient

    On 2) I know I must use taylors expansion, but up to how many terms, and what do I do once i get there?
  2. jcsd
  3. Apr 5, 2010 #2


    Staff: Mentor

    I doubt it very much. I don't see anything in your work that indicates you took partial derivatives. Your textbook should have some examples of categorizing critical points by the use of partials.
    I don't think a Taylor series has anything to do with this problem. The comment I made before applies here as well.
  4. Apr 5, 2010 #3
    The only examples I found using partials considered the second derivative at the given point, however as the questions states the second derivative at the points are all 0, hence all the examples I have found give an inconclusive solution... that is why I have become unstuck, but if I take third derivatives at the point (0,0) there are some non zero solutions, but I am unsure how to identify them as max, min, saddle...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook