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Topic: Enrichment
Replies: 38   Last Post: Aug 24, 2012 1:33 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Enrichment
Posted: Aug 21, 2012 9:29 PM

> Mike's function, f(x) = (x-1)(x-2) / (x+1)(x+2),
>
> 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.
>\
> 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

Date Subject Author
8/15/12 Peter Duveen
8/15/12 Robert Hansen
8/15/12 Robert Hansen
8/15/12 GS Chandy
8/16/12 Peter Duveen
8/17/12 Robert Hansen
8/16/12 Haim
8/17/12 GS Chandy
8/17/12 GS Chandy
8/17/12 Peter Duveen
8/17/12 Robert Hansen
8/17/12 Louis Talman
8/17/12 Robert Hansen
8/17/12 Wayne Bishop
8/17/12 GS Chandy
8/17/12 Peter Duveen
8/18/12 Robert Hansen
8/18/12 GS Chandy
8/18/12 Peter Duveen
8/19/12 Robert Hansen
8/19/12 Peter Duveen
8/19/12 Robert Hansen
8/22/12 kirby urner
8/20/12 Dave L. Renfro
8/21/12 kirby urner
8/23/12 Robert Hansen
8/23/12 Robert Hansen
8/23/12 Robert Hansen
8/21/12 Peter Duveen
8/21/12 Robert Hansen
8/22/12 Wayne Bishop
8/22/12 Robert Hansen
8/21/12 Peter Duveen
8/22/12 Robert Hansen
8/22/12 Peter Duveen
8/22/12 Dave L. Renfro
8/22/12 Dave L. Renfro
8/24/12 Dave L. Renfro
8/24/12 Robert Hansen