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.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Maximum of rational functions

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