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Math Help - Extrema

  1. #1
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    Extrema

    Hello,

    yesterday we had a test of calculus and one question was:

    Find and classify the extreme of
    h(x,y)=(1+1/(x))*(1+1/(y))*(1/(x)+1/(y))

    I have absolutely no idea how to solve this thing. Can someone help me?

    Greets,
    Leslon
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by Leslon View Post
    Hello,

    yesterday we had a test of calculus and one question was:

    Find and classify the extreme of
    h(x,y)=(1+1/(x))*(1+1/(y))*(1/(x)+1/(y))

    I have absolutely no idea how to solve this thing. Can someone help me?

    Greets,
    Leslon
    An extrema is a local minimum or maximum within a function. This is when f'(x)=0

    You have h(x,y) = \left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\righ  t)\left(\frac{1}{y}+\frac{1}{x}\right)

    Let's first try to simplify this...

    h(x,y)=\left(1 + \frac{1}{y} + \frac{1}{x} + \frac{1}{xy}\right) \left(\frac{1}{y}+\frac{1}{x}\right)

    h(x,y)=\frac{1}{y} + \frac{1}{y^2} + \frac{1}{xy} + \frac{1}{xy^2} + \frac{1}{x}+\frac{1}{xy}+\frac{1}{x^2}+\frac{1}{x^  2y}

    h(x,y)=\frac{1}{y} + \frac{1}{y^2} + \frac{2}{xy} + \frac{1}{xy^2} + \frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^2y}

    Can you derive this?
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  3. #3
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    Well if I derive this, I get:
    -(1+1/y)*(1/x+1/y)/x^2-(1+1/x)*(1+1/y)/x^2 for dh(x,y)/dx

    and

    -(1+1/x)*(1/x+1/y)/y^2-(1+1/x)*(1+1/y)/y^2 for dh(x,y)/dy

    and now I'm stuck..

    What to do next??

    PS: I've included a .tex file if necessary
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  4. #4
    Eater of Worlds
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