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Point of inflection

  1. Apr 30, 2013 #1
    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. jcsd
  3. Apr 30, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

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

    ##\frac{x^2}{x-1} = x^2 (x-1)^{-1}##
     
  4. Apr 30, 2013 #3

    Mark44

    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.
     
  5. Apr 30, 2013 #4
    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.
     
  6. Apr 30, 2013 #5

    Mark44

    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?
     
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