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Math Help - To find Max/Min on a closed function

  1. #1
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    To find Max/Min on a closed function

    Find local Max/Min of the function z=f(x,y) = (2x-x^2)(2y-y^2) by finding the critical points of F and then classifying each critical point as to whether it is a local max or local min or saddle point.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Is your question about the general method or this problem in particular?

    If it is generally how do you find and classify local extrema see attachment where I have answered a similar question
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  3. #3
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    to find local max/min z=f(x,y)= (2x-x^2)(2y-y^2)
    do I multiply the function first??
    or just the the partial diff as it is?
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  4. #4
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by fearless901 View Post
    to find local max/min z=f(x,y)= (2x-x^2)(2y-y^2)
    do I multiply the function first??
    or just the the partial diff as it is?
    You'll get the same answer either way. Do what's easiest. I'd recommend taking as is, because when you take the partial w.r.t x, (2y-y^2) is a constant and vice versa.
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