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: Finding Stationary Points

  1. Jan 7, 2014 #1
    1. The problem statement, all variables and given/known data
    See attached for problem

    Attempt at solution

    ∂f/∂x = 3x2+12x
    ∂f/∂y = 3y2-12y



    x=0 or,
    3x+12 = 0 → x= -4


    y=0 or,
    3y-12=0 → y=4

    I find the next stage difficult, because there are no mixed terms in the polynomial any of the values i substitute into another gives me 0, because of this i need help finding the stationary points, I'm fine with classifying them


    Attached Files:

    • 1.png
      File size:
      7.9 KB
  2. jcsd
  3. Jan 7, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I don't see the difficulty. You have two values for x and two for y. How many combinations does that give for (x, y)?
  4. Jan 7, 2014 #3
    This just gives me two stationary points doesn't it?
  5. Jan 7, 2014 #4
    I see, it is 4, i thought there would be other values i would need, so my points would be


    Is this correct?
  6. Jan 7, 2014 #5


    User Avatar
    Science Advisor

    If you had had "mixed" terms, xy, then you would have equations with both x and y leading to the result that a specific value of x leads to a specific value of y. Here, that does not happen. The derivative with respect to x will be 0 if x= 0 or -4 no matter what y is. The derivative with respect to y will be 0 if y= 0 or 4 no matter what x is. In particular, both derivatives will be 0 at (0, 0), (0, 4), (-4, 0), and (-4, 4) as you say.
  7. Jan 7, 2014 #6
    Thanks, that explanation helps me understand that better
  8. Jan 7, 2014 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Yes, those are the stationary points. As for classification: have you taken (multivariate) second-order tests yet?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted