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Math Help - Finding CP using Partial Derivatives

  1. #1
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    Finding CP using Partial Derivatives

    The equation is this
    B = e ^(xy/2)

    I have successfully found all 6 first and second order partial derivatives but need help finding the CP [/FONT]
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  2. #2
    Senior Member Pinkk's Avatar
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    I assume you mean critical point? If that's what you're talking about, then (a,b) is a critical if (a,b) is in the domain of f(x,y) and:

    1) \frac{\partial f}{\partial x}(a,b)=\frac{\partial f}{\partial y}(a,b)=0

    OR

    2) one or both of \frac{\partial f}{\partial x}(a,b) and \frac{\partial f}{\partial y}(a,b) are undefined.

    In the case of f(x,y)=e^{\frac{xy}{2}}:

    \frac{\partial f}{\partial x}=\frac{ye^{\frac{xy}{2}}}{2}
    \frac{\partial f}{\partial y}=\frac{xe^{\frac{xy}{2}}}{2}

    Knowing this, (0,0) must be a critical point because \frac{\partial f}{\partial x}=0 when y=0. Similarly, \frac{\partial f}{\partial y}=0 when x=0. Since e^{\frac{xy}{2}} can never equal 0, the only critical point is (0,0).
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