The discussion revolves around analyzing the function f(x) = x^2 / (x - 1), focusing on identifying asymptotes, extrema, and points of inflection.
Some participants have provided suggestions for alternative approaches to deriving the first derivative. There is ongoing exploration of the conditions for points of inflection, with differing interpretations of the implications of the second derivative's behavior at specific points.
Participants are navigating the complexities of derivative calculations and the definitions of points of inflection, with some uncertainty about the implications of their findings.
Write this as an equation, and use parentheses.mathpat said:Homework Statement
x^2 / x-1. Identify any asymptotes, extrema and points of inflection.
As an equation, this is f'(x) = x(x-2)/(x-1)2.mathpat said:Homework Equations
The Attempt at a Solution
I am stuck trying to derive my first derivative. My first derivative equals 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.mathpat said: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?
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?mathpat said:I see... so basically that means there is no point of inflection since I can not set that equation equal to zero and solve?
mathpat said:By the way, I appreciate both of your help.