1. The problem statement, all variables and given/known data Skethch the greaph of x^3/(x^3+1). Identify all extrema and points of inflection, asymptote equations, and easily found intercepts 2. Relevant equations If a/b=0, a must be 0.(thats how I got critical points from first derivative) And chain rule: F'(x) = f '(g(x)) g '(x) And so on. 3. The attempt at a solution What I have to do is to find points of inflection, asymptotes, and critical points. And I took the first derivative using Quotient rule and got 3x^2/(x^3+1)^2 I am going to take the second derivative of my original function to get ponts of inflection, but I am stuck. As you can see, f'(x) = 3x^2/(x^3+1)^2 And I pondered a bit for I think I need to use chain rule because of that (x^3+1)^2 in the denominator. But how should I use it? what about the numerator? I can't just use chain rule in the denominator, and use power rule in nominator on my own, right? I have a bad feeling about this. This is what I will get if I apply power rule in nominator and apply chain rule in denominator: 6x/[2(x^3+1)(3x^2)] This is wrong, right? because I treated numerator and denominator by using different rules on each of them. Can you check this for me? What should I do in order to get the second derivative? Or can I just ignore the denominator and just take Quotient rule again to get derivative?