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Math Help - Study question about Curve Sketching.

  1. #1
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    Study question about Curve Sketching.

    Ok so I have a test on curve sketching coming up, and I can't seem to get around how to do this question.

    It says

    Sketch the curve for the function y= (x^2+11x-22) / x^2
    Include intercepts, extreme values, points of inflections and any other significant details.

    When I start taking the derivative and expanding, I get some funky answers, its hard to see what im doing wrong.
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  2. #2
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    Quote Originally Posted by Skor View Post
    Ok so I have a test on curve sketching coming up, and I can't seem to get around how to do this question.

    It says

    Sketch the curve for the function y= (x^2+11x-22) / x^2
    Include intercepts, extreme values, points of inflections and any other significant details.

    When I start taking the derivative and expanding, I get some funky answers, its hard to see what im doing wrong.
    Let me give you a hint that will help you a lot.

    \frac{x^2+11x-22}{x^2}=\frac{x^2}{x^2}+\frac{11x}{x^2}-\frac{22}{x^2}=1+\frac{11}{x}-\frac{22}{x^2}=1+11x^{-1}-22x^{-2}
    Thus, now taking the derivative is incredible simple.
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  3. #3
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    You know, I know all about that, but I never figured about using it, thanks.
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  4. #4
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    Quote Originally Posted by Skor View Post
    You know, I know all about that, but I never figured about using it, thanks.
    Thus,
    y'=-11x^{-2}+44x^{-3}=0
    Multiply by through,
    x^3,
    -11x+44=0
    x=4.
    Thus, the derivative is zero at four.
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