# Point of inflection

1. Apr 30, 2013

### mathpat

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

x^2 / x-1. Identify any asymptotes, extrema and points of inflection.

2. Relevant equations

3. The attempt at a solution

I am stuck trying to derive my first derivative. My first derivative equals x(x-2)/(x-1)^2. I tried to use the quotient rule again using while incorporating the chain rule and after multiple attempts I kept resulting with 2 / (x-1)^3.

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

2. Relevant equations

3. The attempt at a solution

2. Apr 30, 2013

### Zondrina

This should help in general, switch your quotient rule into a product & chain rule :

$\frac{x^2}{x-1} = x^2 (x-1)^{-1}$

3. Apr 30, 2013

### Staff: Mentor

Write this as an equation, and use parentheses.

f(x) = x2/(x - 1)
As an equation, this is f'(x) = x(x-2)/(x-1)2.
Your answer is correct, and this can be verified by calculating the derivative using the technique that Zondrina suggested.

4. Apr 30, 2013

### mathpat

I see..... so basically that means there is no point of inflection since I can not set that equation equal to zero and solve?

By the way, I appreciate both of your help.

5. Apr 30, 2013

### Staff: Mentor

The sign of f'' changes at x = 1. If x < 1, f''(x) < 0, and if x > 1, f''(x) > 0. Does this mean that there is an inflection point at x = 1? Why or why not?