XPost: sci.math, sci.math.symbolic   
   From: marsh@privacy.net   
      
   On Mon, 4 Jan 2005, Fred the Wonder Worm wrote:   
      
   > Dr. Muhammad Masroor Ali  wrote:   
   >>   
   >> I have four quadratic equations of the form,   
   >> y = a x^2 + bx + c, where 0 <= x <= 1.   
   >>   
   >> I need to find the maximum and minimum values of y (from four values)   
   >> for each point in the range of x ([0.0,1.0]). I know that I can plot   
   >> the equations and find the result visually. But is there a way of   
   >> solving this analytically?   
   >>   
   >> The situation is further complicated by the fact that not a single   
   >> equation gives the min (max) value in that range, the lines do   
   >> intersect and the equation giving min (max) do change.   
   >   
   > I _think_ that the other followups I have seen have missed the point.   
   > Either that, or I have. :)  I assume that you mean that you have four   
   > quadratic functions (call them f1,f2,f3,f4), and for each point x in   
   > [0..1] you are interested in the following two values:   
   >   
   >    g(x) = Min(f1(x), f2(x), f3(x), f4(x))   
   >    h(x) = Max(f1(x), f2(x), f3(x), f4(x))   
   >   
   min(x in [0,1]) { f1(x), f2(x), f3(x), f4(x) }   
      
   = min{ min(x in [0,1]) f1(x), min(x in [0,1]) f2(x)   
    	min(x in [0,1]) f3(x), min(x in [0,1]) f4(x) }   
      
   So finding min over [0,1] for each f separately is the first   
   step in finding min over [0,1] for all f's.   
      
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