1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Concavity of a rational function

  1. Jun 29, 2011 #1
    I have to curve sketch this function, ((x)3))/((x)2-1)

    I did all of the steps, and I got this as the second derivative: ((2x(x2+3))/((x2-1)3)

    I got concave up:(-1, 0)u(1, inifinity)

    Concave down:(-infinity, -1)u(0,1)


    Am I right?

    I use -1 and 1 as the interval since they are the asymptotes.
     
  2. jcsd
  3. Jun 29, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Hi realism877! :smile:

    That is correct.
     
  4. Jun 29, 2011 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    To have a more complete sketch, how does the function behave for |x| → ∞ ?

    Where are inflection points and relative extrema?
     
  5. Jun 29, 2011 #4
    the point of inflection is (0,0)
     
  6. Jun 29, 2011 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    To see how the function behaves for |x| → ∞, it might help to write [itex]\displaystyle \frac{x^3}{x^2-1}\ \ \text{ as }\ \ x+\frac{x}{x^2-1}[/itex]
     
  7. Jul 3, 2011 #6
    The local max=(-sqr(3), -2.598)

    Local min=(sqr(3), 2.598)

    Correct?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Concavity of a rational function
  1. Concave Function (Replies: 1)

  2. Rational Functions (Replies: 8)

  3. Concave Functions (Replies: 3)

  4. Rational function (Replies: 6)

Loading...