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Thread: Stationary points of a Multivariate function

  1. #1
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    Stationary points of a Multivariate function

    How do I find the stationary points. I find the constants making it difficult to simplify?
    And what does part c mean?

    Stationary points of a Multivariate function-sketch-6-.png

    This is my working so far.

    Stationary points of a Multivariate function-sketch-7-.png
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  2. #2
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    Re: Stationary points of a Multivariate function

    I do not get y= \left(\frac{5}{a}\right)^{\frac{1}{1- a}}x.

    From 5y- ax^{a- 1}y^a= 0, 5y= ax^{a-1}y^a.

    Divide both sides by y^a; 5y^{1-a}= ax^{a- 1}.

    Divide by 5: y^{1- a}= \frac{a}{5}x^{a- 1}.

    Take the 1- a root: y= \left(\frac{a}{5}\right)^{\frac{1}{1- a}}x^{\frac{a-1}{1-a}}= \left(\frac{a}{5}\right)^{\frac{1}{1- a}}x^{-1}.

    That is, x^{-1}, not x.
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  3. #3
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    Re: Stationary points of a Multivariate function

    And how would you do part c, which needs to find a hyperbola?
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  4. #4
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    Re: Stationary points of a Multivariate function

    ..
    Last edited by mathfn; May 17th 2017 at 08:27 AM.
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