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Thread: Help Finding Concave up of a large rational function

  1. #1
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    Question Help Finding Concave up of a large rational function

    Greetings.

    f(x)= (x^2-4)/(x^2+3x+2)
    f'(x)= (3x^2+12x+12)/(x^4+6x^3+13X^2+12X+4)
    f''(x)= (-12x^5-42x^4-6x^3+120x^2+48)/(x^8+6x^7+13x^6+12x^5+4x^4)

    So far I have:

    x Int= (-2,0)
    Horizontal Asymptote= 1
    Vertical Asymptote= Does Not Exist

    I need f(x) is concave up on the interval(s)=

    As you can see the double prime is nasty, and I don't know how to simplify it in order to help me find the concave up intervals. Any help or direction would be appreciated.

    Thank you.
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  2. #2
    Senior Member
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    Feb 2010
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    Try to simplify f: {x^2-4\over x^2+3x+2} = {(x+2)(x-2)\over(x+1)(x+2)}.
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