# Derivatives and graphs

1. Dec 9, 2007

### Hurricane3

1. The problem statement, all variables and given/known data

y=(2x+1)/$$\sqrt{x^2+1}$$

Find where are the asymptotes, where is it increasing increasing/decreasing, ect.....

2. Relevant equations

3. The attempt at a solution
when I took the first derivative (im trying to find where it increases/decrease), I got
dy/dx = $$\frac{2x^2-x+2}{(x^2+1)\sqrt{x^2+1}}$$

but there isn't any roots for this function... so what does that mean?

Last edited: Dec 9, 2007
2. Dec 9, 2007

### CocaCola

No vertical asymptotes as x^2+1 can never be 0.

No horizontal asy as (x^2)^1/2 is one, and 2x is one.

Slant asymptote is synthetic division (x^2+1)^(1/2) |2x+1

If there are no 0's then that means that the equation always increases or decreases.

3. Dec 10, 2007

### HallsofIvy

Staff Emeritus
Grammer police: Better would be "either always increases or always decreases".

Any graph that does not have a horizontal line segment "always increases or decreases"!