# Thread: Info for function f(x)=x^2/(x-1)

1. ## Info for function f(x)=x^2/(x-1)

First, thanks for any help. It's been a couple of decades since I have tried any college math, but I'm back in school and I'm attempting to finish a degree and trying to understand how to get some info on the function f(x)= x^2/(x-1).
1. All extrema
2. Inflection points
3. Intercepts
4. Asymptotes.
5. Show concave structure and note any discontinuities

I can simply get the results using Maple 11 software, but can't understand how to get there.

Thanks !

2. Originally Posted by rocktguy
First, thanks for any help. It's been a couple of decades since I have tried any college math, but I'm back in school and I'm attempting to finish a degree and trying to understand how to get some info on the function f(x)= x^2/(x-1).
1. All extrema
2. Inflection points
3. Intercepts
4. Asymptotes.
5. Show concave structure and note any discontinuities

I can simply get the results using Maple 11 software, but can't understand how to get there.

Thanks !
Extrema = local max/min/absolute max or min

1. $f'(x)=\dfrac{2x(x-1)-(1)(x^2)}{(x-1)^2} = \dfrac{x(x-2)}{(x-1)^2}$

To find local min or max is when the derviative is zero. so...

$0=x(x-2) x=0,2$ then you look at the interval less then zero, bewteen 0-1,1-2, and >2 to see if its max or min. You plug in numbers in each of these intervals to see if the function is neg. or pos. In this case, at x=0 it is a local min. and at x=2 it is a local max.