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Math Help - please help me with this question. 5 dollars for correct answer!!

  1. #1
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    please help me with this question.

    Thinking about the shape of the graph (no calulus needed), what is the largest
    value of f(x,y) = 1/(1+x^2+y^4)?
    Last edited by apatite; February 10th 2013 at 11:52 AM.
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  2. #2
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    Re: please help me with this question. 5 dollars for correct answer!!

    Well this one is easy, is obviously that f(0,0) = 1 is the highest value.
    Otherwise if x or y increase in any direction from the origin (positive or negative), f will decrease exponenttialy.
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  3. #3
    Senior Member Paze's Avatar
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    Re: please help me with this question.

    Quote Originally Posted by apatite View Post
    Thinking about the shape of the graph (no calulus needed), what is the largest
    value of f(x,y) = 1/(1+x^2+y^4)?
    If no calculus is needed, then why on earth are you posting in 'calculus'?
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  4. #4
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    Re: please help me with this question.

    Quote Originally Posted by Paze View Post
    If no calculus is needed, then why on earth are you posting in 'calculus'?
    That thought occurred to me, too.

    Assuming x and y are real numbers, x^2 and y^4 are nonnegative, so the largest possible value is clearly f(x,y)=1 at (x,y)=(0,0) as draganicimw observed. One rather trivial correction - f does not decrease exponentially away from the origin; its decrease is only polynomial.

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