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Re: Enrichment
Posted:
Aug 21, 2012 9:29 PM
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> Mike's function, f(x) = (x-1)(x-2) / (x+1)(x+2),
> is a quadratic divided by a quadratic.
>
> Jean Gaston Darboux, "Discussion de la fraction
> (ax^2 + bx + c)/(a'x^2 + b'x + c')", Nouvelles
> Annales de Mathematiques (2) 8 (1869), 81-86.
> http://books.google.com/books?id=jRgAAAAAMAAJ&pg=PA81
>\
> Those interested in a challenge might want to consider
> how you can use non-calculus concepts (quadratic formula
> and max/min of parabolas topics) to investigate where
> the graph of y = (ax^2 + bx + c)/(dx^2 + ex + f) has
> a local maximum value and/or a local minimum value.
> We begin by rewriting the equation in implicit form
> as a quadratic expression in the variable x:
>
> x^2y + 3xy + 2y = x^2 - 3x + 2
>
> (y-1)x^2 + 3(y+1)x + 2(x-1) = 0
>
I got lost with the words "We begin by rewriting the equation..."
Which equation again? Not Mike's. Not Darboux's.
I wasn't able to find an equation in x and y only, that's being rewritten.
Kirby
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