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Homework Help: 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
    Hi realism877! :smile:

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

    SammyS

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    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

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    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?
     
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