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Critical Points of a function

  1. May 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Find all the critical points of f(x,y) = 2x^3+xy^2+5x^2+y^2+100

    2. Relevant equations



    3. The attempt at a solution

    I'm really not sure how to do this question due the the x^3 term in the function. Could someone please advise how to start this.

    Thanx :D
     
  2. jcsd
  3. May 24, 2007 #2

    Dick

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    The critical points are where the partial derivatives of f with respect to x and y vanish simultaneously. Why should the x^3 be a problem?
     
  4. May 24, 2007 #3
    Partial derivatives

    (6x^2+y^2+10x)i + (2xy+2y)j

    how am i supposed to find values of x and y that make it equal to zero??

    the partial derivative with respect to x is a quadratic function with both x and y terms. so i'm stuck!!
     
  5. May 25, 2007 #4

    Pythagorean

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    You have two components and you can set each to zero. Then you have two equations and two unknowns.
     
  6. May 25, 2007 #5

    Dick

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    You shouldn't really have components anyway. The partial derivatives aren't a vector. Start with the second one 2xy+2y=0.
     
  7. May 25, 2007 #6
    Arent critical points those where either first derivative is 0 or not defined ?
     
  8. May 25, 2007 #7

    Pythagorean

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    good point.
     
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