Expert: Jack Cheng - 12/15/2006

Question
f (x) = x^2 - 2x + 3 / x - 2 , Df = R1 {2}

a) find eventual virtual zeros
b) find eventual asymptotes
c) draw the graph
d) Find f'(x)

Answer
Hi Eric,

I am not familiar with some of the terms and symbols you are using, like eventual asymptotes, eventual virtual zeros, the Df = R1{2), etc.

However, here's how to find the function's derivative:

f(x)  = (x^2 - 2x + 3) / (x - 2)
f'(x) = [Dx (x^2-2x+3) * (x-2) - (x^2-2x+3) * Dx(x-2)]  / (x-2)^2
     = [(2x-2)(x-2) - (x^2-2x+3)] / (x-2)^2
     = (2x^2 - 6x + 4 - x^2 + 2x - 3) / (x-2)^2
     = (x^2 - 4x + 1) / (x-2)^2

The function also has a vertical asymptote at x=2.

Sorry that I can't help any further.

~ Jack