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Math Help - Finding extrema based on a function

  1. #1
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    Let f be the function given by f(x) = 3ln(x^2+2)-2x with domain [-2,4].

    a) Find the coordinate of each relative maximum and minimum point of f. Explain your answer.

    I understand that I have to find the first and second derivative.
    For the first derivative I got \frac {-2x^3+2x}{x^2+2}

    For the second derivative I got \frac{-2(x^4+7x^2+2)}{(x^2+2)^2}
    I was just wondering if that was right.

    I also had to find the x-coordinate of each point of inflection. Am I right when I say that i need to do sign analysis for the second derivative to find the points of inflection?

    Thanks,
    -Chris
    Last edited by mr fantastic; November 23rd 2009 at 06:03 PM. Reason: Merged posts
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  2. #2
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    Quote Originally Posted by Chris22 View Post
    Let f be the function given by f(x) = 3ln(x^2+2)-2x with domain [-2,4].

    a) Find the coordinate of each relative maximum and minimum point of f. Explain your answer.

    I understand that I have to find the first and second derivative.
    For the first derivative I got \frac {-2x^3+2x}{x^2+2}

    For the second derivative I got \frac{-2(x^4+7x^2+2)}{(x^2+2)^2}
    I was just wondering if that was right.

    I also had to find the x-coordinate of each point of inflection. Am I right when I say that i need to do sign analysis for the second derivative to find the points of inflection?

    Thanks,
    -Chris
    f'(x) = \frac{6x}{x^2+2} - 2 = \frac{-2(x^2-3x+2)}{x^2+2}
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