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Differentiation problem

  1. Nov 8, 2005 #1


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    I'm trying to complete the question below:
    Consider F(x,y)=1/3x^3+y^2+2xy+2x+2y+1
    Find the 2 stationary points of F and show that one of them is a minimum of F.
    I've got as far as getting:
    dF/dx = 2/3x+2y+2
    dF/dy = 2x+2y+2
    I would like to know what i need to do next (do i have to treat the above two terms as simultaneous equations?)
    Any help will be appreciated
  2. jcsd
  3. Nov 8, 2005 #2


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    Homework Helper

    Be careful, if your initial function F(x,y) is correct then you've got a wrong partial derivative with respect to x. I see a x³/3 and its derivative should give x² and I don't see that term in your dF/dx. dF/dy seems to be correct.

    Once you have the right partial derivatives, let them equal zero and solve them together (system of 2 equations). This gives the stationary points.
  4. Nov 8, 2005 #3


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    Thanks for your reply,

    You're correct, it should read:

    dF/dx = 2/3x^2+2y+2, which i wrote down in my notes!Typo error.

    When you say, solve them together, do you mean like you do with simultaneous equations?

    I tried that route but i'm getting confused with what to do with the term that's a fraction.

    I get:



    so i assume that the 2 term cancels,as does the 2y and then i get lost.
  5. Nov 8, 2005 #4


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    Yes, a system of equations so simultaneous equations.
    By the way, (x³/3)' = x² and not 2x²/3...

    Be careful with your derivatives, else the stationary points will be wrong too of course!
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