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Maximum of rational functions

  1. Feb 6, 2005 #1
    Suppose 2 cuadratic functions: ax^2+bx+c, dx^2+ex+f. Suppose that the first one is upside with its minimum above the x line reference, and the second one is downside with its maximum above the x reference, and suppose that the two functions intersect at two points that pass through straight line gx+h.
    My question is
    ¿could the maximum of (dx^2+ex+f)/(ax^2+bx+c), be splitted as the
    max( (dx^2+ex+f)/(gx+h))*max((gx+h)/(ax^2+bx+c))?

    I dont know how to put drawings here, but i hope the argument has been clear to understand
    I was tryng some numeric examples in my pc and the result was positive, but i dont know what is the general proof. Thanks for your comments
  2. jcsd
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